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Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

28 September 2026

13 essays on what a pair is for, many pictures at once, measuring from one picture, the rectangle behind the lens, drawn confidently, what each system gave up, the eye that moves, the second projection, what a machine computes, the real instrument, the second eye, mirrors that are not cameras and through water and glass

What a pair is for

A facade matched a column out comes forward, not back

A railing matched one post along is rebuilt 2.2 times further away. A facade of windows 2.4 metres apart cannot be: a one-column shift that way needs a negative disparity, and the only mistake left in front of the cameras brings the facade to 6.3 metres from twenty, a third its size, hanging 1.1 metres off the ground with nothing under it to sink into. Its corners hold it only if the wall is assumed flat. Two corners then convict it at every period; one corner and a drainpipe need the pipe half a metre in for windows and four and a half for a fine repeat.

7 figures Many pictures at once

A length fixes the scale where it lies, and the worst camera nowhere

Move one measured metre round a ring of twenty-four cameras and the worst camera hardly notices: 199 to 225 millimetres on the open walk, 80 to 103 on the closed loop, wherever the bar lies. What moves is the scale. On the open walk a length is known to 0.41 per cent beside the bar and 1.58 per cent twenty walls away, and no longer bar at the start brings the far end below 1.53. A survey that must measure lengths everywhere on an open walk needs its references spread along it; one that closes its loop can put a single reference anywhere.

6 figures Measuring from one picture

A plumb wall tells a slope from a horizon, faintly

A sloping ground and a misplaced horizon fail the ground's depth test alike. A wall standing plumb beside the ground separates them in kind: a slope leaves the wall's test at 1e-16, and a horizon moves it. But it moves it a tenth as far as it moves the ground's — 0.20 per cent for a horizon five pixels out, against 2.11 — so a pair of windows a metre wide cannot see the difference, and a whole facade six metres wide can tell a one-degree slope from its matching horizon 95 times in a hundred. A wall running straight away from the camera sees nothing at all.

5 figures The rectangle behind the lens

A rolling frame on a bend is a coarse curvature gauge

Read row by row on a bend, a frame leans every vertical by an amount proportional to one over its range less one over the bend's radius, so posts at several ranges lie on a straight line that crosses zero at the radius — exactly, to a thousandth of a metre. Off the axis the zero moves to R·cos of the bearing, the circle on which a camera on a bend is sharp. As a gauge it is coarse: one frame's eight posts read a 50 m bend as 45 m (35–74) with tops placed to half a pixel, and sixteen frames as 51 m (47–55). The slower the sensor reads, the better it measures the road.

6 figures Drawn confidently

A steady creep draws the rule's bow

The arc reading was built to find the constant-ratio rule by the shape its pavements bow the diagonal. A correct pavement painted by a hand that lets each transversal gap grow 4.5 per cent on the last bows it the same way — to 0.31 pixels, a cosine of 0.9994 — on eight braccia, and 1.5 per cent is enough on twenty-two. The arc reading measures how much a pavement's tiles lengthen, not what lengthened them, and against its counterfeit it is a coin. The rule's own definition still tells them apart: its gaps' logarithms are straight, a correct pavement's bend. Read to half a pixel, that names the rule on eight braccia 94 times in a hundred.

5 figures What each system gave up

A stepped hand passes for a tiring one on a short strip

A painter who steps dividers from each row to the next leaves an error that accumulates — a walk from the edge begun at, with no fatigue in it. The fit of habit and creep takes about four-fifths of that walk before any reading of the scatter starts, because a walk is slow and so are the two numbers. What is left names the starting edge nearly as well as fatigue does, and on a six-bay strip it cannot say which of the two mechanisms left it: the verdict needs twenty-four bays on one strip, or sixteen six-bay strips by one hand.

6 figures The eye that moves

A vehicle's pitch lags the road by its wheelbase

A camera fixed to a vehicle does not pitch with the road under it; it pitches with the chord between its wheels. Over a step from level to six per cent, a two-slit scroll's rows — silent on any steady grade — depart by up to 2.18 rows over 6.5 metres of road for a 2.7-metre wheelbase, against 4.26 over 4.0 for a camera that pitched at the point. The excursion's width is the eye's own chord plus about the wheelbase, and one line of posts reads the wheelbase back to ±8 centimetres. A vertical curve does not silence the rows either; it shrinks them as one over its length.

5 figures The second projection

An even spend of the panel is an uneven picture

A keystone correction that spends the panel evenly exists: render the picture straight into the panel pixels that reach the corrected rectangle, one sample each. At fifteen degrees that is 82.2 per cent of a frame's samples, and on the wall it delivers exactly what a full frame does — 0.99 of the source's detail at the near edge, 0.76 at the far — because the panel, not the source, was setting the detail everywhere. It removes no unevenness. On fewer samples it makes the picture worse where it was worst; the even picture is a uniform source of 57.6 per cent of a frame.

5 figures What a machine computes

Ground and sky meet at the horizon without a crack

A ground of rate triangles and a sky of direction triangles share their vertices along the horizon, and rasterised as a graphics processor does it — positions snapped to a fraction of a pixel, every centre given to one triangle by the top-left rule — they lose no pixel and claim none twice, at any roll and any snapping. What the horizon does have is a sliver: a centre that falls within half a snapping step of it goes to whichever side the snapped edge puts it, and one that falls exactly on it, rolled one way, is given to the ground at a weight of zero. A ground stopped at a far plane leaves the crack the shared vertex never does: f·h/D rows.

6 figures The real instrument

One focus stopped down is as sharp as six in a deep room

Refocusing a room panorama frame by frame costs a seam of 12.9 arcminutes on a fixed head. One focus stopped down costs none of that, and at f/40 holds half a metre to four metres to 5.27 arcminutes — sharper than the fixed head's seam, blunter than a tracking head's 2.82. But the comparison flatters refocusing: the frame on the table also holds the wall behind it, so it cannot be held sharper than 5.27 however it is focused. Counted properly, one focus on a plain head comes within 2.4 per cent of the geared one, and pays for it in light.

6 figures The second eye

Steering swings a camera too little to see ahead

A vehicle yaws about its rear axle, so a camera mounted ahead of the axle is swung sideways whenever the vehicle steers — a real baseline, where a turn alone gave the blind point ahead nothing. Half a degree of yaw swings a windscreen camera 1.3 centimetres and a bumper camera 3.1. Straight ahead at eight metres a pixel then costs 96 and 40 per cent of the depth. The cost falls as one over the arm times the yaw, and a usable 10 per cent needs 7.2 metre-degrees: two degrees of steering every frame on a bumper. Ordinary lane-keeping gives a fraction of that.

5 figures Mirrors that are not cameras

The wall convicts a pair set too wide

A window set wider than its partner's reflection keeps every joining line on the mirror's point, so the one test a symmetric photograph was known to carry cannot see it. The wall the other pairs fix can: it says where the partner should be seen, and a window set ten centimetres too wide misses by 6.0 pixels. With marks read to 0.4 px it convicts a 3-centimetre offset eight or nine times in ten and a 5-centimetre one every time. What no single photograph can see is a move along the camera's own ray to the window.

6 figures Through water and glass

Turning the glass tells the window from the lens

A calibration done through a two-degree wedge of glass reports a lens decentred by about 1e-2 that does not exist, and hides the glass inside it. Calibrate twice with the glass turned between, and the glass's part turns while the lens's stays: a half turn finds a real lens decentring of 2.2e-3 to 5.2e-4 with readings to 0.4 px, where one calibration was 1.0e-2 out. Three calibrations spread evenly round the turn do better, because the loop the glass traces is not a circle. What never separates is the radial coefficient, which has no direction for a turn to carry.

5 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

27 September 2026

13 essays on the eye that moves, through water and glass, what a pair is for, the real instrument, the rectangle behind the lens, what a machine computes, what each system gave up, the second eye, measuring from one picture, the second projection, many pictures at once, mirrors that are not cameras and drawn confidently

A band lifted by columns bends its lines — the eye that moves
A calibration through glass reports a prism — through water and glass
A railing matched one along stands underground — what a pair is for
A refocused panorama is six lenses — the real instrument
A rolling frame on a bend is right at its centre — the rectangle behind the lens
A sky is carried as a direction — what a machine computes
A strip's scatter points to the end drawn last — what each system gave up
A turn moves the picture, not the blind point — the second eye
A wrong model shows at its own level — measuring from one picture
Keystone correction spends the panel unevenly — the second projection
Two short bars are not one long one — many pictures at once
Two wide pairs are most of a symmetry — mirrors that are not cameras
The rule's bow is read by its shape — drawn confidently

26 September 2026

12 essays on the rectangle behind the lens, the second eye, what a pair is for, what each system gave up, through water and glass, the real instrument, the eye that moves, the second projection, what a machine computes, many pictures at once, mirrors that are not cameras and drawn confidently

A frame's shear knows travel only over depth — the rectangle behind the lens
A plane's coefficient reaches as far as its parallax — the second eye
A rectification's free shift is free only near the pair — what a pair is for
A strip keeps its ratio, not the end it began — what each system gave up
A third eye sees the water the pair cannot — through water and glass
A tilted target pays for its tilt in perspective — the real instrument
An eye that pitches with the road keeps its rows — the eye that moves
Drawing for the curve removes the curve, not the nearness — the second projection
One homography makes a shadow map the eye's picture — what a machine computes
Split the track and the needles turn — many pictures at once
Two people between mirrors see each other equally often — mirrors that are not cameras
A straightedge convicts the rule on five braccia — drawn confidently

25 September 2026

10 essays on what each system gave up, the rectangle behind the lens, many pictures at once, the eye that moves, what a pair is for, the real instrument, the second eye, what a machine computes and through water and glass

A tiring hand draws a different habit — what each system gave up
A dolly zoom off the axis keeps a line, not a plane — the rectangle behind the lens
A scale bar is worth its ends, not its tape — many pictures at once
A scroll of a climbing road measures its grade — the eye that moves
A sliding pair keeps its line only near the middle — what a pair is for
A stereographic fisheye is a division model — the real instrument
A sway gives the blind centre a depth, not a good one — the second eye
A texture reaches the horizon as a rate — what a machine computes
A tiring panel keeps its order, not its direction — what each system gave up
A wedge moves the centre, not the lens — through water and glass

23 September 2026

10 essays on the rectangle behind the lens, the real instrument, through water and glass, the second eye, the eye that moves, what a machine computes, what a pair is for, many pictures at once, the second projection and drawn confidently

A camera on a bend is sharp on a circle — the rectangle behind the lens
A known target sharpens the fit and does not separate it — the real instrument
A fit weighted by the miss trusts only the surface — through water and glass
A parallax length is a height over a depth — the second eye
A seam that bends trades a turn for a gap — the eye that moves
One warped shadow map, and what it cannot reach — what a machine computes
Rectifying a pair spends what its epipolar lines lean — what a pair is for
The cameras decide where a narrow view settles — many pictures at once
A curved screen tilts a stereo pair both ways at once — the second projection
A turned cube punishes the eye, not the construction — drawn confidently

20 September 2026

8 essays on the eye that moves, what each system gave up, what a machine computes, the real instrument, through water and glass and what a pair is for

A shadow decides which landscape it is — the eye that moves
The rows count hands, not cameras — what each system gave up
A tilted span walks a staircase — what a machine computes
A vanishing line with a slope in it — what each system gave up
No design separates the two coefficients — the real instrument
The residual does not warn — through water and glass
The second disparity cuts cells — what a pair is for
Where a seam is allowed to go — the eye that moves

17 September 2026

7 essays on what each system gave up, many pictures at once and drawn confidently

The rows under a splay measure the bays, not the lean — what each system gave up
A loop's far side is a length — many pictures at once
A survey is trusted at its own accuracy, unless its error has a shape — many pictures at once
A start needs the sign of its depths, not their size — many pictures at once
A tapered part meets at its apex — drawn confidently
A square plan is not a cube — drawn confidently
The rule is exact for a floor that lengthens — drawn confidently

15 September 2026

7 essays on what each system gave up and the eye that moves

A camera count needs a tolerance — what each system gave up
One camera means one horizon, not one point — what each system gave up
A scroll can be asked its own radius — the eye that moves
The tenth row has neither — what each system gave up
The exclusion is two conditions, not ten rows — what each system gave up
The stations are also a staircase — the eye that moves
A seam breaks direction, not size — the eye that moves

14 September 2026

15 essays on the real instrument, what a pair is for, many pictures at once, drawn confidently, through water and glass, mirrors that are not cameras and measuring from one picture

A model that inverts has a horizon instead of a fold — the real instrument
A third ray is worth what its picture is worth — what a pair is for
The spread a point gets — many pictures at once
A cylinder has two different ends — drawn confidently
The response is at the ends and the information is not — the real instrument
The stick a stereo pair puts back — through water and glass
Vergence moves the shells and does not respace them — what a pair is for
A third eye that lands on the next post — what a pair is for
Focusing moves the pivot past its best place — the real instrument
The wedge recovered with the camera — through water and glass
Two mirrors show fewer images than they make — mirrors that are not cameras
Two mirrors are three cameras — mirrors that are not cameras
A symmetric object is its own stereo pair — mirrors that are not cameras
Closer than they appear, by a factor with a number in it — mirrors that are not cameras
Where each closure enters the stratification — measuring from one picture

12 September 2026

19 essays on many pictures at once, the eye that moves, the second eye, the rectangle behind the lens, what a machine computes and the second projection

An uncertainty is quoted from something — many pictures at once
The eighth held number bends the scene — many pictures at once
A narrow view keeps a second answer, inside out — many pictures at once
A scale chain leans rather than wanders — many pictures at once
A scroll round a bend loses its straight-line depth — the eye that moves
Closing a loop mends its ends — many pictures at once
Two marks off a known plane find the other eye — the second eye
A turning frame can be straightened; a travelling one cannot — the rectangle behind the lens
Along a line of constant depth the page is affine — what a machine computes
An epipole in the picture leaves a blind disc — the second eye
A point at infinity is an ordinary vertex — what a machine computes
The two pencils keep one number — the second eye
Turning and travelling blur different worlds — the rectangle behind the lens
A dolly zoom is a step and a zoom, and they meet at one depth — the rectangle behind the lens
A shadow map's texels land by two distances and two cosines — what a machine computes
Rectification is a family, not an operation — the second eye
A close picture carries its own distance — the rectangle behind the lens
Seeing the scene fences in the plane at infinity — the second eye
A stereo picture is drawn for a level head — the second projection

11 September 2026

18 essays on what each system gave up, what a pair is for, the real instrument, the eye that moves, through water and glass and the rectangle behind the lens

A yes in the table is a price — what each system gave up
A page is bounded by a divide, not a centre — what each system gave up
The midpoint is a choice of ruler — what a pair is for
A barrel model folds at a radius it sets itself — the real instrument
A pond in a scroll is not an ellipse — the eye that moves
Four surfaces, and no one camera that draws them — what each system gave up
Whole pixels cut space into shells — what a pair is for
A scroll through two slits ranges in a straight line — the eye that moves
A tilted sensor is not a distortion — the real instrument
Both coordinates agree on a circle and a line — what a pair is for
A point under water has two depths — through water and glass
Raise the gaze, and the line is gone — what a pair is for
The lines that calibrate a lens — the real instrument
A mismatch on its own line needs a third eye — what a pair is for
A straight stick in water is a kink and a curve — through water and glass
Focusing is a zoom — the rectangle behind the lens
The entrance pupil walks with the angle — the real instrument
A wedge of glass turns the camera behind it — through water and glass

6 September 2026

50 essays on the eye that moves, drawn confidently, systems that kept the measure, surfaces that are not flat, constructing a view, light and mirrors and what survives

A landscape that changes its rule halfway up — the eye that moves
A mirror that is not parallel to the wall — drawn confidently
The minor axis is not the axle — drawn confidently
The workshop that throws drawings away — systems that kept the measure
A grid on the wall is a scale without a projection — systems that kept the measure
Higher on the page, and where that stops being true — systems that kept the measure
No solid casts an aspective figure — systems that kept the measure
Two stations in one picture — systems that kept the measure
The room a divergent picture is a photograph of — systems that kept the measure
What a removed wall costs that a removed roof does not — systems that kept the measure
Where a surface spends its pixels — surfaces that are not flat
The horizon's shape belongs to the surface — surfaces that are not flat
A pole is a line — surfaces that are not flat
The kink at a seam — surfaces that are not flat
Dividing to a point off the board — constructing a view
Shot on one surface, shown on another — surfaces that are not flat
The bays that are not equal — constructing a view
Which rule a fisheye obeys, from straightness alone — surfaces that are not flat
The eye is a picture surface too — surfaces that are not flat
What a straightedge reaches on a receding line — constructing a view
The arcs the five-point construction actually draws — surfaces that are not flat
Two rules for one pavement — constructing a view
A soft shadow on a curved floor is not the lamp's image — light and mirrors
The hole a rig cannot fill — surfaces that are not flat
The stair that turns has a vanishing point that moves — constructing a view
A measuring point for a ramp — constructing a view
A projector that is not at the dome's centre — surfaces that are not flat
The lamp's size over its distance, and nothing else — light and mirrors
Figures on a street that slopes — constructing a view
How many lamps make one lamp — light and mirrors
The centre of the picture is not the centre of the paper — constructing a view
What a point in shadow can see of the sky — light and mirrors
Copying square by square — constructing a view
Four points on a conic look the same from anywhere on it — what survives
The lamp a low shadow cannot locate — light and mirrors
The hook is the centre, and the eye is not — constructing a view
Three conics are one conic and a choice of horizon — what survives
Where a shadow splits in two — light and mirrors
How many shadows determine the object — light and mirrors
Pascal's line, and the theorem underneath Pappus — what survives
A dent breaks the terminator — light and mirrors
The triangle a camera cannot move — what survives
A curved surface made of straight lines — what survives
A shadow edge read as a profile — light and mirrors
A line is a closed curve — what survives
The lamp and the floor cannot both be recovered — light and mirrors
Three kinds of map on a row of posts — what survives
Every projectivity is two perspectivities — what survives
The picture contains what is behind the camera — what survives
The theorem that is obvious one dimension up — what survives

1 September 2026

20 essays on the eye that moves, through water and glass, mirrors that are not cameras, measuring from one picture and systems that kept the measure

Three distances in one landscape — the eye that moves
One surface, two images — through water and glass
A ball of water has no eye either — through water and glass
One shutter, two views — mirrors that are not cameras
Two matches are enough — mirrors that are not cameras
An area, out of one photograph — measuring from one picture
Square to the camera is the worst mirror — mirrors that are not cameras
The same person, twice on one panel — systems that kept the measure
Counting is a measurement — measuring from one picture
Size that means rank — systems that kept the measure
Two mirrors make one turn — mirrors that are not cameras
A picture in bands — systems that kept the measure
An angle on the ground — measuring from one picture
The corner that answers every eye — mirrors that are not cameras
The answer is an ellipse — measuring from one picture
The pond with its trees laid flat — systems that kept the measure
What survives being copied — systems that kept the measure
Which reference to measure from — measuring from one picture
The floor a better camera cannot reach — measuring from one picture
Five facts that close the same gap — measuring from one picture

31 August 2026

20 essays on the second eye, many pictures at once, the rectangle behind the lens, what a pair is for, the real instrument, drawn confidently, what a machine computes and what survives

A flat scene fixes no second eye — the second eye
Far enough away, a pair is one eye — many pictures at once
The centre has an area — the rectangle behind the lens
The depth a pair calls zero — what a pair is for
How flat is flat enough — the second eye
The hole a scene actually sees — the real instrument
The sharp band is a decision — the rectangle behind the lens
A pupil sees around an edge — the rectangle behind the lens
Seven marks, three answers — the second eye
The corner sees an ellipse — the rectangle behind the lens
The surface two pictures cannot separate — the second eye
An ambiguity is not an uncertainty — the second eye
Six tangents and the point nobody drew — drawn confidently
The disc and the streak — the rectangle behind the lens
One depth per sample is not enough — what a machine computes
A point and a line are one object — what survives
The horizon has a pole — what survives
Five tangents name the same conic — what survives
Desargues read the other way — what survives
The quadrilateral that finds the middle — what survives

30 August 2026

20 essays on the real instrument, drawn confidently, the second projection, surfaces that are not flat, constructing a view, the other systems, where to stand and light and mirrors

The lens a pavement can hide — the real instrument
The rule that draws another room — drawn confidently
Matching buys one seat — the second projection
The distance at which the eyes part — the second projection
Drawn for the cylinder, shown on the cylinder — surfaces that are not flat
Three conditions, and three prices — surfaces that are not flat
The surface a screen wants — surfaces that are not flat
Three procedures, one panel — constructing a view
A picture that can be printed — surfaces that are not flat
Four marks before anything is said — constructing a view
The slip that leaves no trace — constructing a view
A picture with no eye — the other systems
One hand step each — constructing a view
A flight that has ends — where to stand
Nothing moves along the direction — the other systems
Stepped, or measured from the zero — constructing a view
One face, one scale — the other systems
What a panel says about its maker — constructing a view
Two distances to infinity — the other systems
The arrangement the count cannot see — light and mirrors

29 August 2026

20 essays on the second projection, what a machine computes, where to stand and light and mirrors

The screen that names the seat — the second projection
The seats a screen will accept — the second projection
A curved screen is eight flat ones — what a machine computes
One picture and three people — the second projection
What the two eyes are sent — the second projection
The evenness a curve buys — the second projection
A projector in the viewer's eye — the second projection
What an eye can paint — where to stand
Facing the reader is not being reachable — where to stand
The eye that reaches the most — where to stand
A design that lands in two rooms — where to stand
The stretch decides the band — where to stand
One flight, two pictures — where to stand
A fold names the height — where to stand
How many lamps a drawing has — light and mirrors
The distance at which two lamps part — light and mirrors
A floor cannot fake a second lamp — light and mirrors
The drawing does not run out of lines — light and mirrors
A lamp behind the camera — light and mirrors
Counting shadows is not counting lamps — light and mirrors

28 August 2026

16 essays on mirrors that are not cameras, through water and glass, where to stand, light and mirrors and what survives

A mirror ball does not know its size — mirrors that are not cameras
The dome knows its offset in units of itself — through water and glass
A pane gives a product before it gives two numbers — through water and glass
The caustic is the mirror's own ruler — mirrors that are not cameras
A fitted radius is wrong before it is uncertain — mirrors that are not cameras
A stair does not use all its faces — where to stand
The residual has a shape — light and mirrors
The floor is a choice of coordinates — light and mirrors
The lamp comes out in rays and not in plan — light and mirrors
The corners a floor cannot add — light and mirrors
A floor is read along curves — light and mirrors
An error with two terms — what survives
What a null result is worth in decades — what survives
The ladder of assumptions is a ladder of conditioning — what survives
The bias out of reach — what survives
A floor with a referent — what survives

26 August 2026

15 essays on measuring from one picture, the second projection, surfaces that are not flat and the other systems

The wall under the paint — measuring from one picture
The curvature a shadow reports — measuring from one picture
The screen is a picture surface too — the second projection
One picture of a ball — measuring from one picture
Two pictures of a ball — measuring from one picture
The dish no outline reaches — measuring from one picture
The pivot that is not the eye — surfaces that are not flat
The parallax you cannot shoot away — surfaces that are not flat
The camera that is a cylinder — surfaces that are not flat
A rig is right on one surface — surfaces that are not flat
The ball a drawing does not draw round — the other systems
No view draws a curved plate true — the other systems
The drawing and the development — the other systems
A drawn fold has a phantom — the other systems
Two outlines are two curves — the other systems

24 August 2026

15 essays on systems that kept the measure, constructing a view and what survives

A picture with two eyes in it — systems that kept the measure
The second eye is a shear — systems that kept the measure
Counting the eyes needs the room — systems that kept the measure
Two grounds, and what the second one costs — systems that kept the measure
A parallel floor under a perspective room — systems that kept the measure
Three-point, laid out with a straightedge — constructing a view
A drawing has three horizons — constructing a view
The arc every eye stands on — constructing a view
The proportion is the assumption — constructing a view
The ball at the edge of the frame — what survives
The quadrilateral no rectangle casts — constructing a view
Every quadric has one outline — what survives
A line is a space of its own — what survives
The map a row of posts is — what survives
Perpendicular is a pairing — what survives

23 August 2026

15 essays on what a machine computes, the second projection, light and mirrors and the other systems

Four numbers and a window — what a machine computes
Turning the cameras inwards — the second projection
A tile is an off-centre frustum — what a machine computes
The near plane can be any plane — what a machine computes
One plane is nearly free — what a machine computes
A wire with a corner in its shadow — light and mirrors
The dimetric the set square draws — the other systems
The edge of a shadow is drawn on the object — light and mirrors
What one oblique drawing shows — the other systems
A circle off the coordinate planes — the other systems
A hole is not preserved — light and mirrors
A shadow across a second object — light and mirrors
The shadow rules that hold here — the other systems
The ball stands at a focus — light and mirrors
The drawing that gives the solid back — the other systems

22 August 2026

15 essays on drawn confidently, constructing a view and where to stand

The third point put where it looks right — drawn confidently
Both vanishing points on the paper — drawn confidently
Which way the drawn circle leans — drawn confidently
The forty-five degree shadow — drawn confidently
Measured down from the waterline — drawn confidently
Carrying a height across the room — constructing a view
A picture with nothing straight in it — constructing a view
The room the eye may stand in — where to stand
An anamorph has one eye — where to stand
Seven is not a power of two — constructing a view
The circle in the square wants a number — constructing a view
The design that outruns the floor — where to stand
The anamorph that crosses a corner — where to stand
The line every nosing is on — constructing a view
The height a flat floor cannot give — where to stand

21 August 2026

15 essays on mirrors that are not cameras, surfaces that are not flat and what survives

A curved mirror has no eye — mirrors that are not cameras
Where the focus went — mirrors that are not cameras
The one shape that focuses — mirrors that are not cameras
A mirror ball is an equal-area fisheye — mirrors that are not cameras
The cone that reads the floor — mirrors that are not cameras
Undoing a picture made on a curve — surfaces that are not flat
How well the floor has to be known — surfaces that are not flat
The floors that unroll — surfaces that are not flat
The third column is area — surfaces that are not flat
Counting cloud by counting pixels — surfaces that are not flat
The conic a circle becomes — what survives
Two lines at infinity — what survives
Five marks and the sixth — what survives
Two circles, one picture — what survives
The polar with a straightedge — what survives

19 August 2026

15 essays on constructing a view, light and mirrors and the other systems

The plane is a choice — constructing a view
Straightening does not move the eye — constructing a view
The horizon, and the fraction — constructing a view
The floor that is not a plane — light and mirrors
The ramp has its own horizon — constructing a view
Three views do not fix the solid — the other systems
A shadow across an edge — light and mirrors
The bay repeated by a straightedge — constructing a view
The view that makes a line a point — the other systems
Nothing moves when the object does — the other systems
The lamp is the second eye — light and mirrors
A light far enough away — light and mirrors
The true shape of a cut — the other systems
Two lamps and one map — light and mirrors
What two parallel views leave free — the other systems

18 August 2026

15 essays on surfaces that are not flat, where to stand and what survives

The arcs a curvilinear drawing uses — surfaces that are not flat
One parameter between two surfaces — surfaces that are not flat
A floor anamorph is three numbers — where to stand
Conformal is not undistorted — surfaces that are not flat
Six flat pictures of everything — surfaces that are not flat
Where the anamorph still works — where to stand
The lines a surface leaves alone — surfaces that are not flat
The marks name the place, not the height — where to stand
An angle is a cross-ratio — what survives
The ceiling that is not a plane — where to stand
A set cut for one eye — where to stand
The two points a picture hides — what survives
One conic calibrates the camera — what survives
What a flat map leaves alone — what survives
Three constructions, one map — what survives

16 August 2026

15 essays on the other systems, light and mirrors and what survives

Any three lines you draw are a cube — the other systems
The shadow of a ball is a conic — light and mirrors
Oblique is a shear, and the shear is the whole system — the other systems
The diagonals find the middle — what survives
The lamp, out of the picture — light and mirrors
A ruler on an isometric drawing — the other systems
A shadow can be un-cast — light and mirrors
Two triangles and the line nobody drew — what survives
A wall does not get darker as it goes away — light and mirrors
The drawing does not say which corner is nearer — the other systems
What one picture of a plane determines — what survives
A lamp lights less than half a ball — light and mirrors
Four lines have a cross-ratio — what survives
The ellipse the drawing office draws — the other systems
The centre, got back out of the picture — what survives

15 August 2026

15 essays on the rectangle behind the lens, what a machine computes and the second projection

A focal length is not an angle — the rectangle behind the lens
The divide is postponed, not avoided — what a machine computes
The screen sets the distance — the second projection
A wide field on a small screen — the second projection
Stepping closer is not zooming — the rectangle behind the lens
What happens behind the eye — what a machine computes
Every row is a different camera — the rectangle behind the lens
The precision a depth buffer has left — what a machine computes
Two pictures on one screen — the second projection
A frame is an interval — the rectangle behind the lens
A pixel is not a point — what a machine computes
The render is distorted on purpose — the second projection
A projector is a camera run backwards — the second projection
A texture does not interpolate on the page — what a machine computes
The pixel that is not square — the rectangle behind the lens

14 August 2026

15 essays on the eye that moves, what each system gave up and systems that kept the measure

A scroll is a camera that moves — the eye that moves
The picture whose lines spread — what each system gave up
What the removed roof buys — systems that kept the measure
A straight line in a scroll is a hyperbola — the eye that moves
An inverse perspective is a leaning plane — what each system gave up
Measuring a room off the page — systems that kept the measure
A centre and a measure are exclusive — what each system gave up
A picture with no size–distance signal — systems that kept the measure
The centre a scroll does not have — the eye that moves
A carpet and the people on it — systems that kept the measure
A map along, and a picture across — the eye that moves
Each system answers its own question — what each system gave up
A scroll is not a panorama — the eye that moves
Assembled from several views — systems that kept the measure
What perspective gave up — what each system gave up

12 August 2026

15 essays on what 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 on the 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 on measuring 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

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