CMISH / Field Studies · Threshold

SAME series

Eighteen studies of what sameness can promise. Change a view, an assumption, a grouping, a connection, or a direction. Watch which conclusions survive.

18 plates · 01–18 measurement · convention · objective · history open any · 1–9 jump · 0 opens 10

Field study 01v0.2 · hosted

SAME N

Same count. Different claims.

What can a shared count promise?

Frozen: N = 1,536
Free: generative story

spherical samplingRandomSobolFibonacci

Fibonacci sphere and equal-area disk, 1536 sites

Fibonacci shown · low spacing variation is one property, not an overall ranking

Fibonacci opens firstOpen →

Field study 02v0.1.2

SAME SHADOW

Same projection. Different bodies.

What did the view discard?

Frozen: one silhouette
Free: the body behind it

occupancy from a projectionPrismGradeWell

Occupied depth sections of the three bodies at y equals zero

Section at y = 0 · identical occupied x extent · Well’s enclosed cavity is visible

Prism opens firstOpen →

Field study 03v0.2.1

SAME EARTH

Same planet. Different frames.

What did the projection change?

Frozen: one sampled surface
Free: projection

measure vs shapeGlobeMercatorEqual Earth

Same spherical disks in Mercator and Equal Earth

Same disks · seam clipping · independently fitted map panels

Globe opens firstOpen →

Field study 04v0.1.3

SAME SITES

Same generators. Different territory.

Who defined nearest?

Frozen: seven generators
Free: metric

nearest-site territoryEuclideanTaxicabChebyshev

Same seven sites · Euclidean, Taxicab and Chebyshev · native 360² rasters

Euclidean opens firstOpen →

Field study 05v0.2.3

SAME SAMPLES

Same samples. Different assumptions.

What does one measurement control?

Frozen: one measured set
Free: interpolating assumptions

model / influenceGlobalLocalPeriodic

Three reconstructions above, and response to a unit change at sample five below

Common axes within each panel · same measured values · different influence

Global opens firstOpen →

Field study 06v0.3.2

SAME VOLUME

Same target budget. Different obligations.

What does better mean?

Frozen: target mean density 0.40
Free: obligation

structure / allocationCarryConductShare

Target 0.40 · achieved means 0.40000000 / 0.40000000 / 0.40001309 · local SIMP results

Carry opens firstOpen →

Field study 07v0.1.2

SAME MARGINALS

Same x. Same y. Different pairing.

What did the separate lists lose?

Frozen: same x, same y
Free: pairing

couplingAlignOpposeScramble

Three pairings of the same x and y values

Same x and y lists · fixed pairing permutations · common axes

Align opens firstOpen →

Field study 08v0.1

SAME AVERAGE

Same averages. Different groups.

Whose weights made the average?

Frozen: 400 records · A 60%, B 40%
Free: group membership

aggregation / weightsAgreeDisappearReverse

Reversal: A leads pooled sixty to forty percent; B leads within both groups

Reverse grouping shown · identical pooled rates · exact integer counts

Agree opens firstOpen →

Field study 09v0.1.2

SAME MAGNITUDE

Same Fourier magnitude. Different structure.

What did magnitude leave out?

Frozen: one Fourier magnitude
Free: phase

spectrum vs structureSourceBorrowedScrambled

Three real reconstructions · one magnitude array · common linear grayscale

Source opens firstOpen →

Field study 10v0.1

SAME LAW

Same rule. Different histories.

What else does a prediction need?

Frozen: update rule · domain · grid
Free: initial position

dynamics / predictionABC

Three exact trajectories at step 32 and their distances from the reference

Step 32 · ε = 2⁻⁴⁰ · below: distance from A, logarithmic scale

Step 32 opens firstOpen →

Field study 11v0.1

SAME MOVES

Same moves. Different place.

What did order change?

Frozen: six rigid motions · λ = 1
Free: composition order

rigid motion / compositionGivenReversedShuffled

All 720 endpoints with given and reversed paths at lambda one

All 720 endpoints · Given and Reversed paths · λ = 1 · fixed equal-unit axes

Given opens firstOpen →

Field study 12v0.1

SAME DIVERGENCE

Same sources. Different flow.

What did the sources leave open?

Frozen: source field ρ · witness flux
Free: divergence-free component

vector fields / underdeterminationQuietSlideSpin

Quiet Slide and Spin velocity fields with identical source and witness square

Shared source and arrow scale · witness flux 1/π² · y increases downward, as in the live exhibit

Quiet opens firstOpen →

Field study 13v0.1

SAME DEGREES

Same neighbors counted. Different worlds.

Can every local count match while the network comes apart?

Frozen: 12 vertices · degree 3 · 18 edges · positions
Free: who connects to whom

networks / reachabilitySpreadNarrowApart

Same degrees: three networks after two hops from A

Source A, two hops · Spread reaches 8, Narrow 7, Apart 6 · every vertex has degree 3 · identical positions and 18 edges

Spread opens firstOpen →

Field study 14v0.1

SAME IMPULSE

Same push integrated. Different motion.

How much does the timing of a push matter?

Frozen: applied impulse · oscillator · starting rest
Free: force timing

forced linear dynamicsEarly pulseBroad pushTwo pulses

Same applied impulse, different oscillator responses

Applied impulse 1 N·s in every case · two pulses 1 s apart · exact responses on fixed axes · residual envelope measured at 3 s

Two pulses · 1 s apart opens firstOpen →

Field study 15v0.1

SAME EIGENVALUES

Same eventual stability. Different excursions.

Does eventual decay mean a disturbance never grows?

Frozen: eigenvalues −1, −2 · start (0, 1) · units · norm
Free: off-diagonal coupling k

linear dynamics / transient growthk = 0k = 4k = 12

Same eigenvalues, different transient norms

k = 0, 4, 12 · peak / initial norm 1.000×, 1.036×, 3.011× · fixed starting vector (0, 1), units, and Euclidean norm

k = 12 opens firstOpen →

Field study 16v0.1

SAME DISTANCES

Same distances. Different handedness.

Can equal distances certify a proper rigid match?

Frozen: six distances; four labels; units
Free: orientation; permission to reflect

distance geometryRotateBest proper fitReflect

Same distances, opposite handedness

The same six distances survive both panels. Left: the global rotation-and-translation minimum retains 1 unit of 3D RMS error. Right: reflection closes the gap. Both use the same projection and scale.

Manual rotation opens firstOpen →

Field study 17v0.1

SAME RESIDUAL

Same residual size. Different error.

Does the same residual size promise the same solution error?

Frozen: matrix A · right-hand side b · residual norm 1 · units
Free: residual direction θ

linear algebra / conditioningFirst axisDiagonalSecond axis

Same residual, different solution error

θ = 45° · relative residual 1.000% · relative error 70.714% · κ₂ = 100 · equal-unit circle and error ellipse

45° diagonal opens firstOpen →

Field study 18v0.1

SAME FIT

Same fitted summary. Different structure.

What did the fitted summary leave out?

Frozen: 11 observations · summary at declared rounding precision · shared axes
Free: arrangement of the observations

statistics / regression diagnosticsQuartet IQuartet IIQuartet IIIQuartet IV

Anscombe’s quartet: matching rounded summaries, different structures

Anscombe’s quartet · 11 points each · lines round to y = 3.00 + 0.50x · actual fitted coefficients differ · variance y agrees at 1 decimal place

all four datasets opens firstOpen →

How to use. Each card opens a full-page exhibit. The top-left ← Series chip returns here. The figures are computed from the study data. Open an exhibit to change its method and inspect a point. Volume solves its three designs when opened; the other exhibits are ready to inspect.