What's new
Essays arrive in groups rather than one at a time, and a group usually opens up a subject the collection had not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.
14 August 2026
15 essays onthe eye that moves, what each system gave up and systems that kept the measure — a subject new to the collection
A scroll is a camera that moves
A Chinese handscroll is not a picture with a wandering viewpoint or a picture with no viewpoint. It is the image of an eye that travels along a track and records one vertical line at a time, and that object has an exact geometry — orthographic along the roll, perspective across it.
What each system gave upThe picture whose lines spread
In a Byzantine icon the sides of a table diverge with depth. The standard account says the vanishing point is behind the viewer. It is not — it sits below the near edge, in front of the eye, and it is the vanishing point of a direction running down and away.
Systems that kept the measureWhat the removed roof buys
The Japanese convention of drawing an interior with its roof lifted off is usually explained as a way of seeing inside. What it actually buys is uniformity — every room reports the same share of its floor, to the last sample, where the eye that frames the same building reports three different numbers.
The eye that movesA straight line in a scroll is a hyperbola
Under a pushbroom the image of a straight world line is a Möbius function of the paper coordinate, which is a rectangular hyperbola. It is straight exactly when the line holds its depth — so a curve in a handscroll is a depth signal rather than a stylistic one, and the sag is computable in pixels.
What each system gave upAn inverse perspective is a leaning plane
Ask a divergent construction what solid it depicts and it answers: a rectangle, four right angles, near edge equal to far. What the splay encodes is not the shape but the plane's tilt — and a real square on a plane leaning toward the camera really does photograph with its far edge wider.
Systems that kept the measureMeasuring a room off the page
A perspective picture of a floor has to be rectified before anything on it can be measured, and the rectification is a fit that amplifies the marking error. An oblique picture of the same floor is already rectified — the page is the plan, at one scale, and a ruler on the paper is a ruler on the ground.
What each system gave upA centre and a measure are exclusive
Eight drawing systems, measured on five questions, with the pinhole as a row rather than the header. Exactly one has a centre of projection and it is exactly the one with no true measure — and loosening the measure test by a hair lets it in, which is what says the boundary is real.
Systems that kept the measureA picture with no size–distance signal
In a system with no diminution the drawn size of an object falls at exactly zero pixels per metre, so nothing in the picture says how far away anything is. Depth has to be carried by something else, and what carries it is height on the page — linearly, and without a horizon.
The eye that movesThe centre a scroll does not have
Fit a common point to the rays of one section of a handscroll and it misses by metres. The miss is not a residual to be tightened — it is exactly the standard deviation of the eye's own track, it grows linearly with how much is unrolled, and it goes to zero only for a section of no width.
Systems that kept the measureA carpet and the people on it
A Persian miniature draws the ground as though from above and the figures standing on it as though from in front. The two views want optical axes exactly ninety degrees apart, and the plan view does not shorten a standing figure — it replaces its height with its distance from the point under the eye.
The eye that movesA map along, and a picture across
The midpoint of a segment lying along a scroll's length images to the midpoint of its image, exactly. The midpoint of a receding one lands 22% of the way off. One projection, two answers — and the direction that keeps measure keeps something a perspective picture never offers.
What each system gave upEach system answers its own question
A comparison in which every system wins its own column proves nothing if the columns were chosen after the systems. The test that makes it a result is whether any system wins something it was not designed for — and two of them do.
The eye that movesA scroll is not a panorama
Both draw straight world lines as curves, and one of them is a projection. A rotating eye keeps its centre exactly however far it turns; a translating eye has none at all. Curvature and centrelessness are independent properties, and conflating them is the standard mistake about both objects.
Systems that kept the measureAssembled from several views
An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.
What each system gave upWhat perspective gave up
The field ends by turning its own battery on the system it has been comparing everything against. Four quantities a pinhole destroys that the other systems keep, each measured on this site's own machinery, and each the price of the one thing perspective has and they do not.
Before that
Everything published earlier, newest first. Titles only — the cards are on the full listing.
12 August 2026
15 essays onwhat a pair is for, the second eye and many pictures at once
- Depth is a reciprocal — what a pair is for
- The image of the other eye — the second eye
- The track and the scene together — many pictures at once
- A point is a line over there — the second eye
- Seven numbers no picture can name — many pictures at once
- The range a pair cannot see past — what a pair is for
- A chain and an adjustment — many pictures at once
- Eight points and the basis they are read in — the second eye
- Two rays that do not meet — what a pair is for
- A turn of the head is not a step sideways — what a pair is for
- Four cameras fit, and one of them can see — the second eye
- Where the adjustment stops — many pictures at once
- A wrong match is not a small error — what a pair is for
- Another picture of the same sweep — many pictures at once
- Two views give shape and no size — the second eye
10 August 2026
15 essays onthe real instrument, through water and glass, drawn confidently, light and mirrors, the other systems, what survives and where to stand
- Straight lines that are not — the real instrument
- What a ray does at a surface — through water and glass
- A lens destroys the invariant — the real instrument
- A picture through water has no viewpoint — through water and glass
- Fitting a lens from straightness alone — the real instrument
- The sixty-degree cone of vision — drawn confidently
- What survives a pane of glass — through water and glass
- The penumbra is the lamp's image — light and mirrors
- The principal point is not the centre — the real instrument
- The sky inside a cone — through water and glass
- Which axis scales are possible — the other systems
- A projection of a projection — what survives
- The eye is a place, not a point — the real instrument
- The port that is not there — through water and glass
- Standing in the wrong place — where to stand
5–8 August 2026
34 essays onmeasuring from one picture, light and mirrors, surfaces that are not flat, constructing a view, the other systems, drawn confidently, where to stand and what survives
- A height, out of one photograph — measuring from one picture
- A shadow is a second projection — light and mirrors
- No picture surface keeps everything — surfaces that are not flat
- One, two and three point are one construction — constructing a view
- Parallel projection is not primitive perspective — the other systems
- The cube that is a box — drawn confidently
- The point you have to stand at — where to stand
- What a projection destroys — what survives
- Dividing depth by eye — drawn confidently
- Flattening a façade out of the photograph — measuring from one picture
- The cylinder, and the price of going all the way round — surfaces that are not flat
- The measuring point, and the step the method leaves out — constructing a view
- What isometric actually means — the other systems
- Where parallel lines meet — what survives
- Where shadows vanish — light and mirrors
- Wide angle is not distortion — where to stand
- A mirror is a second camera — light and mirrors
- Anamorphosis is only a viewpoint — where to stand
- Recovering the camera from the picture it drew — what survives
- Stereographic keeps every angle, and only stereographic — surfaces that are not flat
- The eye taken to infinity — the other systems
- The horizon is at eye level — if the picture plane is vertical — constructing a view
- The plan hidden in the photograph — measuring from one picture
- Alberti draws a pavement, and chooses where the reader stands — constructing a view
- Every fisheye is a different rule — surfaces that are not flat
- The circle whose centre moves — what survives
- The one thing a single view cannot give — measuring from one picture
- When the picture surface is not flat — where to stand
- An anamorph at true size, on paper — where to stand
- How wrong a measurement from one picture can be — measuring from one picture
- The distance point is the viewing distance, drawn — constructing a view
- What a 360-degree photograph actually is — surfaces that are not flat
- Brunelleschi drilled a hole in his panel — constructing a view
- The cylindrical mirror unbends it — where to stand