V2 V1 V3 · Sonnet

Estate boundaries in Kampinos

Is it really the same boundary?

An old sketch does not land on today’s grid by itself. Someone picked pairs of points that they judged to be the same place and calculated the overlay. Do it on the model: switch points on, spoil one of them and see what is left of the certainty of the boundary.

This is a model in arbitrary units [a.u.], not a plan of Głusk or a map. The historical documents are further down and share no geometry with it.

Diagram of the model: a sketch of an old boundary overlaid on a reference grid Teaching diagram, not a map. Step 1: five points in the fit, RMSE approx. 29.8 a.u. Numerical details are in the summary and in the point register.

Model · arbitrary units · not a map

RMSE 29.8 a.u. · n = 5

Black outline: sketch A after being overlaid on reference grid B (grey). Carmine: the residual, that is, the segment from the point’s place on the grid to the place where it ends up after the fit. Residual vectors at scale ×1, the same as the grid.

  • grid point in the fit
  • point outside the fit
  • boundary close to an active point
  • boundary without point control
  • point residual
Residual vectors:
RMSE at the points
29.8 a.u.
Points in the fit
5 of 6
Boundary segments close to a point
5 of 6

Residuals grow: one point does not fit the others

RMSE is 29.8 a.u.; the largest residual is P4. Note P4: its residual is smaller than its deviation without it. A wrong point pulls the fit towards itself, so the residual alone does not give it away. Point control covers 5 of 6 boundary segments; the remaining 1 segment is drawn dotted because it lies further than 80 sketch units from an active point.

Fit: 1 sketch unit = 2.05 grid units · rotation -2.2° (positive: clockwise in the drawing)

Without scripts the bench is inactive. The drawing shows step 1 of the model. Results of the three steps (approximate values, from the model’s calculations):

  1. Step 1. P1, P2, P3, P4 (shifted by +80 a.u.) and P6: RMSE approx. 30 a.u., largest residual at P4.
  2. Step 2. P1, P2, P3 and P6: RMSE approx. 1.6 a.u., but P4 lies approx. 79 a.u. from the place predicted from the other points.
  3. Step 3. Only P1 and P6: RMSE not assessed, because two points give zero residuals by construction.

Sequence in three steps

Step 1. Five points, including P4 shifted by +80 a.u. from its place on the grid. The fit reconciles all points at once and therefore spreads the error of P4 over the others.

Common points: is it the same object?

Tick the pairs that go into the fit. Residual r: the distance between the point’s place on the grid and the place where it ends up after a fit that includes it. From the others: the same distance when the fit was built without that point. A large difference between the two gives away a point that pulls the result towards itself. The names and ‘identification’ are assumptions of the model.

  • residual r—from the others—
  • residual r—from the others—
  • residual r—from the others—
  • residual r—from the others—
    +80 a.u.

    P4 takes part in the fit: every shift changes all the residuals. A plus sign moves the point right and down, a minus left and up (grid units; the length of the shift equals the slider value).

  • residual r—from the others—
  • residual r—from the others—

What this result says and what it does not

The numbers above describe a model in which we know the ‘true’ places of the points on the grid. When working with a real plan we know only as much as can be justified. Four caveats that can be seen in the drawing.

  1. RMSE speaks about the points, not about the boundary.

    It is the square root of the mean of the squared distances between a point’s place on the grid and the place where it ends up after the fit. It describes the agreement of the chosen pairs. If someone takes two different places for the same object, the RMSE can be small and prove nothing. This page does not label it as the accuracy of the boundary.

  2. Two points always fit.

    The overlay has four unknowns: scale, rotation and two shifts. Two pairs of points give four equations, so the residuals come out as zero by construction. This is a lack of any means of checking, not high quality. That is why for n = 2 the result is ‘not assessed’, not 0.

  3. Between the points there is no measurement.

    A boundary segment far from an active point is an extrapolation. The model draws it dotted when its midpoint lies further than 80 sketch units from the nearest active point. The threshold is a convention of the model, not a statistical result. Paper deforms unevenly, and a single scale and a single rotation will not capture that.

  4. A wrong point pulls the fit towards itself.

    The least-squares method does not know which point is wrong. It spreads the disagreement over all of them, so the residual of a wrong point can be smaller than its deviation ‘from the others’. Switching a point off brings the RMSE down, but it does not settle whether the right object was identified.

Overlay of the sketch on the grid (2D similarity, ‘Helmert’), least squares:
  X′ = u·x − v·y + X₀        Y′ = v·x + u·y + Y₀
  scale s = √(u² + v²) [grid units per 1 sketch unit],  rotation = atan2(v, u)
Residual of point i:  rᵢ = |(X′ᵢ, Y′ᵢ) − (Xᵢ, Yᵢ)|
RMSE = √( Σ rᵢ² / n ),  given only for n ≥ 3
‘From the others’: the same distance for a fit built without point i

What is not here. V2 drew a red ‘band of residual scatter’ (RMSE × 1.25, at least 8 a.u.). This model does not determine a confidence interval, so such a band would look like a statistic that it is not. It was replaced by two things calculated directly: the ‘from the others’ column and the dotted segments without point control.

Reading room: three testimonies about Głusk and Kampinos

The model above shares no geometry with them. Below are only descriptions and reference numbers taken from the references carried over from V2. In this work neither the originals nor the links were opened, so the agreement of the descriptions with the sources needs checking and a historical-geodetic consultation.

  1. 1789 AGAD · Cartographic collection · 131-15 Boundary plan

    Głusk, 1789

    The Archiwum Główne Akt Dawnych (Central Archives of Historical Records) holds a plan of the boundary of the village of Głusk dated 1789. The guide of Kampinos National Park (KPN) recalls that the village remained the property of Polish monarchs until the end of the 18th century.

    What the source confirms

    The plan is a starting point for studying the boundary of Głusk. Begin with the title, the date and the place names. The mere existence of a line on the plan does not prove that a road, a ditch or the edge of a forest runs there today.

    Question for the field: can this line be found today?

    Look for recurring names and for points that can be recognised on both maps. Only fitting the whole sheet will make it possible to select segments for observation. Do not treat today’s forest edge as ready-made confirmation.

    Relation to the model: this plan is not in the drawing. Fitting it would require verified pairs of points and an assessment of the error, not merely an impression of agreement.

    Sources: AGAD inventory, ref. 131-15; KPN guide, p. 3.

  2. late 18th century KPN · exhibition guide · p. 3 Map of a starosty

    The Kampinos starosty

    The KPN guide points to a copy of a map of the Kampinos starosty from the end of the 18th century, made by the Prussian surveyor Kramm. It also states that this map was not reprinted in the exhibition.

    What the source confirms

    The description concerns a starosty, and so a different subject from the boundary of a single village. Setting the titles side by side helps in choosing the right source: the plan of Głusk answers a question about the village, while the starosty map calls for a broader comparison.

    Question for the field: the sheet itself first

    The guide confirms that the map exists, but it does not replace reading it. Before pointing to traces, one has to find a reproduction and check the markings and the extent. We do not assign the geometry of the plan of Głusk to this map.

    Relation to the model: we do not overlay it on the plan of Głusk. It is a different sheet with a different extent, so an attempt could produce apparent geometric contradictions that are a result of the question, not evidence.

    Source: KPN guide, p. 3. The card refers to the description, not to a reproduction of the map.

  3. 1821 AGAD · Cartographic collection · 291-3 Marsh plan

    The wetlands of Kampinos, 1821

    ‘Plan błot w ekonomii narodowej Kampinos położonych’ [Plan of the marshes situated in the Kampinos national estate] dates from 1821. According to the KPN guide it shows the central belt of wetlands: alder woods and mineral islands with fields and meadows.

    What the source confirms

    A change of marking from forest to meadow tells us about the landscape. It is not enough to identify a property boundary. This document helps to check whether, in interpreting an old plan, we are confusing a division of land types with a division of estates.

    Question for the field: what does today’s forest edge say?

    Note the transition between forest and open space, but leave its origin as an open question. Compare the dates of the documents and the types of terrain. Observing a single present-day line does not confirm the course of the boundary from 1789.

    Relation to the model: according to the KPN description the plan concerns the natural and economic structure of the marshes, so the line of an alder carr is not automatically the line of an estate.

    Source: KPN guide, p. 9, plate V.

Three questions before you call a trace in the field a boundary

  1. Name. Write down its old spelling. Similar-sounding places are not enough to identify a location. Check the neighbours and the context of the whole sheet.
  2. Line. Read what it separates: ownership, administrative units or types of terrain. This cannot be established from the colour of the stroke alone. A legend and a description are needed.
  3. Change of land use. A field, a meadow and a forest can occupy the same place in turn. Today’s edge of the trees therefore need not reproduce a boundary from the 18th century.

When comparing with present-day terrain, one first has to fit the scan to a modern map and assess the error of that fit. Only then is it worth choosing observation points. In this reading room no ditch or road is given the status of a confirmed boundary.

Sources and limits of this page

Source references (from V2)

What this page does not know or do

  • All the coordinates in the drawing are invented for the purposes of the model. They do not come from any plan or measurement.
  • There is no scan here with reproduction rights, so the drawing is a diagram, not a reproduction of a document.
  • The links to AGAD and KPN and the descriptions of the documents were not opened or compared with the originals in this work. The identity of the points and the scope of interpretation require a historical-geodetic consultation.
  • The descriptive thresholds (5 a.u. and 25 a.u. for RMSE, 80 sketch units for segment control) are conventional and serve only for the captions in the model.
  • A ditch, a row of trees or the edge of a forest does not prove an estate boundary, and a geometric fit does not replace a source.
What changed from V2 and why
  • Band of residual scatter (RMSE × 1.25): removed, because it looked like a confidence interval. It was replaced by the ‘from the others’ column and the dotted segments.
  • Two separate sheets A and B: combined into one drawing, because the difference is visible only in the overlay.
  • Four variants and a ‘research mode’: cut down to three steps and a manual choice of points.
  • The ‘metric of the selected point’ panel: the numbers were moved into the rows of the register, next to the checkbox.
  • RMSE ‘0.0 a.u.’ for two points: replaced by the label ‘not assessed’, because a lack of data is not zero.
  • Copying the protocol, printing the sheet, notifications and local saving: removed as adding no knowledge. Nothing is saved on the device.
  • Document selection and reading modes: all three testimonies are visible at once and work without scripts.
  • Kept: the 2D similarity transformation, the residuals, RMSE, point P4 with the error slider, the content of the three cards and the source references.