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Orthogonal

·4 mins

A Range Bar is a fixed price increment. Each bar represents the same amount of price movement — say, five ticks. What varies is the time it takes to complete. In a fast-moving market, bars form quickly. In a sluggish one, they take longer. The chart strips away time in exchange for uniform price increments.

A Constant Volume Bar is a fixed number of trades. Each bar completes after the same count of market transactions. What varies is how much price moved during those trades — sometimes a lot, sometimes barely anything. The chart strips away price variation in exchange for uniform transactional activity.

In a system I came across, a practitioner in oil futures uses both simultaneously. His entry signal fires only when both representations show the same thing at the same moment. The key indicator is velocity: does the Range Bar form faster than its average? If yes, and the Constant Volume Bar shows a matching signal — something real is likely happening. If only one representation signals, he ignores it.


The design logic is clean. Each representation removes one variable precisely to make another observable.

Range Bars remove price variation. Time becomes the signal. Constant Volume Bars remove transactional variation. Price movement becomes the signal.

Together they create orthogonal measurements of the same underlying event. Neither measurement alone is sufficient. Their agreement is.

The inversion is equally useful. A Range Bar velocity signal without Constant Volume confirmation says: price is moving fast, but transactional activity isn’t accelerating. That’s a specific failure mode — a false breakout, a structural move without participation, a trap. The non-agreement doesn’t mean nothing; it means something specific and diagnosable.

He built a system that can see its own failure modes.


This pattern appears in science wherever the thing being measured is complex enough to hide.

Exoplanet detection uses two orthogonal methods. Radial velocity measures the star’s Doppler shift — does the star wobble toward and away from us, pulled by an orbiting body? Transits measure photometric dimming — does the star’s brightness dip periodically as something crosses its face? The two methods see perpendicular aspects of the same orbital geometry. When both confirm the same period, confidence is high. When they disagree, the disagreement guides investigation rather than ending it.

Medical imaging works similarly. MRI shows soft tissue through magnetic resonance of water molecules. CT shows density through differential X-ray absorption. Each representation is calibrated to different tissue properties. When both modalities agree on the location and shape of an anomaly, clinicians trust the finding. When they disagree, the disagreement is itself diagnostic: it tells you something about the nature of what you’re looking at.

Auditory neuroscience uses interaural time differences and interaural level differences — the tiny time lag and volume difference between your two ears — to localize sound in three dimensions. Neither cue alone is sufficient for precise localization. Together they triangulate. The brain computes both in separate neural circuits and integrates them. The spatial resolution is better than either channel could achieve.


The principle underlying all of this: orthogonal representations reveal topology.

A single measurement is a projection. You’re seeing the three-dimensional shape from one angle, and you get a two-dimensional shadow. Add a perpendicular measurement and you get a different shadow. Together the two shadows constrain the possible shapes that could produce both of them. Each additional orthogonal view narrows the space of possibilities further.

“Orthogonal” doesn’t mean “independent.” The Range Bars and Constant Volume Bars represent the same market events. They’re not measuring different things; they’re measuring the same thing from perpendicular angles. The orthogonality is about the axis of variability each representation holds fixed — price versus transactional activity — not about the underlying subject matter.

The result is that convergence across orthogonal measurements says something stronger than either measurement alone. And divergence is no longer failure; it’s information about the geometry of the thing being studied.


The practitioner’s Rule 1: signals are only taken when they appear on both representations simultaneously.

This is an epistemological commitment embedded in a rule. It’s a statement about what constitutes sufficient evidence. Not “the Range Bar says yes,” not “the Constant Volume Bar says yes,” but “both orthogonal views of the same market event agree.”

Confidence scales with the independence of the measurements and the degree of convergence. One measurement from one angle: a projection. Two measurements from perpendicular angles: a constraint. More measurements from more angles: topology.

Designing a system with this structure doesn’t just improve signal quality. It changes what the system can know about its own errors. A system with a single measurement has no mechanism to detect its blind spots. A system with orthogonal measurements can observe the failure modes that emerge as non-agreement.

He built the failure mode detector into the architecture of the system. Not as a post-hoc check, but as the central logic.