The Wikipedia page for Orthogonality says that:
“In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity. Although many authors use the two terms perpendicular and orthogonal interchangeably, the term perpendicular is more specifically used for lines and planes that intersect to form a right angle, whereas orthogonal is used in generalizations, such as orthogonal vectors or orthogonal curves.”
There is an interesting 2026 book by Ian Bogost titled The Small Stuff: How to lead a more gratifying life. A Google Books preview from it goes through page 27. The book has the following sections and chapters:
Preface: What If Contentment Were Easy?
The Sensory Enchantment of Everyday Life
C01 The Small Stuff 7
C02 Happiness, Satisfaction, Gratification 20
C03 The Problem with Marshmallows 28
How You Got Dematerialized
C04 The Decline of Sensory Life 43
C05 Why You Can’t Open Doors 50
C06 You Can’t Control What You Do Not Own 58
C07 Working Anywhere Means Working Nowhere 66
C08 Every Place Is the Same Now 75
C09 Adrift in the Data Sea 83
C10 Automated Away 92
The Path Back to Gratification
C11 Reclaiming Sensory Life 105
C12 Heap Wonder on Everything 115
C13 Get a Haircut Every Day 126
C14 Talk About Anything 137
C15 Keep Some Junk Around 147
C16 Live Your Life Sideways 155
C17 Spend Your Day in Its Moments 164
Conclusion: Build a Relationship with Everything 177
In Chapter 16, Live Your Life Sideways, Ian says on page 157:
“A concept from mathematics, which my colleagues in engineering, computer science, and even game design have borrowed, can help explain that feeling and offer lessons for applying it to gratification in your downtime. The idea is called orthogonality, and its just a fancy name for a perpendicular – such as a line intersecting another at a ninety-degree angle. Applied to more concrete domains than geometry, one thing is orthogonal to something else when it contains distinct elements that complement but do not interfere with those of the other.
Consider the difference between chess and checkers. Both games are played on the same grid. In checkers, every piece moves in an identical way, forward in a diagonal. Even when you ‘king’ a checker by reaching the other side of the board, it still moves in the same way, just backward, too. But in chess, the pieces move in varied ways. Pawns and rooks can both move forward, but rooks can move forward as much as they want, until reaching an obstacle. Bishops can move diagonally. And knights move in that distinctive, L-shaped way -they can also jump over pieces.
The relationships between the different chess pieces are orthogonal. Rooks and pawns move along one axis, bishops along another one, the queen and king across both, and the knights according to a different logic entirely. The combination of all these creates the strategic depth that characterizes chess. Whether it is a better game than checkers is not the point; rather, orthogonality makes chess feel bigger, richer, and more complex.
Orthogonality can help explain all sorts of phenomena, even some that are not deliberately designed to be orthogonal. Fashion works well when it is orthogonal. If you want to look good but vary your dress for different styles, seasons, and situations, then you want a supply of separates and accessories that you can combine in creative ways. You can dress down a pair of jeans with a T-shirt and sneakers or dress it up with a shirt or blouse and a jacket or sweater, along with a pair of pumps, boots, or loafers. Capsule wardrobes, which first became popular in the 1970s, have been revived as a way to mix and match more easily, economically, and ecologically. Capsule outfits are composed of core pieces, often in neutral tones, that can be worn alongside colorful or style-specific accents.
Food, too, benefits from orthogonality. Sweet things are beneficially offset by saltiness; fatty ones by the freshness of citrus. A gooey or wobbly dish such as flan is improved by a complementary crunchy element, such as a shard of toffee. Delightful though a schnitzel or a steak might be, their brownness benefits from accompaniment by creamy white mashed potatoes and a forest of green asparagus. Contrast is good. A thing is better alongside its complement. Your life is better when it includes a version of itself done sideways.”
Page 161
“….Othogonality – the art of living your life sideways – is not meant to create hard rules or unbreakable guidelines. As you search for gratifying complements in your life, focus less on the output of the practices you undertake than on the moment-to-moment experience of doing them. That’s where orthogonality lives, in the sensory encounters, not in the work or leisure itself.”
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