Al-Karaji's levelling and tunnel-alignment methods

Before water reaches a field, workers need a route that neither rises against its flow nor loses its direction underground. In The Extraction of Hidden Waters, Abu Bakr al-Karaji describes levels and surveying procedures within a manual following water from exploration to maintenance and handover ¹. A later manuscript introduces levels the author says he devised, followed by a frame-and-plumb diagram ². This is a particular contribution to an older tradition, not the invention of groundwater or qanats themselves.

This record concerns an engineering method, not one machine doing every job. The manual treats levelling, heights and alignment, with diagrams and explanations of instruments; the modern study distinguishes these from soils, excavation and maintenance ³. Levelling means comparing elevations against a reference, not making every water route perfectly horizontal without a gradient.

The contextual qanat is a gently sloping underground tunnel bringing water out by gravity, with vertical shafts for working, access and maintenance ⁴. Its problem differs from a pump's: choose and check the route rather than raise water with an engine. This simplified description does not make every tunnel in every country identical to the manuscript designs.

The 2020 study places qanats in traditions far older than Karaji and discusses their earlier spread; it does not credit him with creating the system ⁴. An author can improve an instrument and explain its reasoning without being the first person to dig a well or measure land. We do not select a single origin date or personal inventor for the entire ancient history of qanats.

Route, soil and excavation were practical problems, not merely a competition for names. The chapter list includes indications of water, soil types, measuring devices, opening tunnels and cleaning them ¹. The world before the author was not an empty space awaiting a solitary genius. Excavators and local knowledge belong to the problem even when these selected leaves do not preserve individual workers' names.

Karaji's principal mathematical works are associated with Baghdad and Buyid patronage; biographies describe later engineering interests after he left, while estimates of his dates and birthplace differ ^{5 6}. We use an eleventh-century context, not an invented exact year for an instrument trial or a canal opening.

The illustrated copy is not from that century. Penn's current catalogue dates its completion to 20 February 1674, whereas the study's captions say 1675; even its bibliography gives the 1674 day while ending the entry with 1675 ^{7 8}. We follow the current institutional catalogue for the copy and preserve the disagreement. A scribe's date is not the author's invention date.

The red heading on 26r introduces levels the text says the author devised, with a drawing forming part of the explanation. That is an attribution within the transmitted work, not an examination of apparatus from his workshop ². The study also discusses inventive levelling and sighting procedures, referring to research on historical surveying instruments ⁹. Author, later copyist and modern interpreters have different roles.

Sunni frame: The study explicitly identifies the named Karaji as a Muslim mathematician and engineer; this is an individual basis, not an inference from name, country or patron ¹⁰. The declared Sunni default in his biography remains distinct from personally attested school membership; the biographies read name no contrary personal affiliation, and Buyid patronage is not recast as Sunni ^{5 6}. This contribution is distinct from his arithmetic of algebraic expressions.

First separate height from direction. A straight tunnel can climb, while one with the intended fall can deviate sideways. The study distinguishes levelling, distance and height instruments from straightness checks and underground sighting ¹¹. One measurement cannot replace another, and knowing an elevation does not establish how much water will be available.

Folio 26r shows a rectangular frame, two raised sight fittings, a triangle and a string ending in a weight; the surrounding text describes a level and determining height ². A plumb line supplies the direction of gravity, and the drawn line provides a comparison reference, not an electronic sensor. We assign no unmeasured numerical accuracy to the picture and do not assume every drawn line represents a separate physical component.

Folio 29r is a geometrical scheme of lines, arcs and letters, not a finished tunnel. The study pairs it with 26r in discussing apparatus and explanation ^{12 13}. Geometry shows relationships rather than every manufacturing detail. Our evidence is selected leaves, not an independent reconstruction of every proof in the book.

Folio 42r shows a sighting arrangement associated with a wooden support, upright and string;45v combines a ruler, caliper-like shape and a bent-route diagram ¹⁴. The study discusses this group in relation to straightness checks, recorded deviations and planning through tortuous conduits ¹⁵. A winding route is not automatically a copying mistake: changing direction is itself a problem requiring description and measurement.

For a paper illustration only, imagine 200 horizontal metres and a 0.4-metre drop. The numerical slope is 0.4/200 = 0.002, or 0.2%, equivalent to two metres per kilometre. These are our modern numbers, not Karaji's measurements or a recommended construction gradient. If two readings have errors with opposite signs, their difference can magnify the error; correct division cannot repair faulty observations. Flow quantity remains a separate question requiring information absent from this exercise.

The study discusses qanats in many regions before and after the author, but the spread of a general technology does not prove that his particular level travelled with every tunnel ⁴. We therefore draw no transmission arrow from this leaf to every country with qanats. Such a link needs evidence for the particular knowledge, not merely a shared water problem.

Textual transmission is clearer: a surviving Penn copy and modern editions, studies and translations listed in the 2020 article, including Persian, French, Italian and an English doctoral translation ^{7 16}. We have not read all these editions. A title in a bibliography is not proof that its entire contents were independently consulted for this page.

The manual's subject rests on inherited qanats, the need for usable water and practical knowledge of ground conditions, as the chapter account shows ¹⁷. In the selected leaves, geometrical lines appear beside string, sighting and drawing procedures: reasoning and work meet rather than occupying sealed worlds ¹⁸.

Calling this a refinement does not establish a teacher-to-pupil chain for every earlier instrument. We create no dependency on another museum invention merely because both use a triangle or plumb line. Distinguishing a familiar principle from an improvement in its arrangement preserves both the inherited knowledge and the boundaries of the author's contribution.

Surviving copies and their instrument drawings allow historical engineering study. The 2020 article refers to Lewis on surveying instruments and Stiros on qanat measurement, using manuscript illustrations to discuss its own topics ¹⁹. Those are references reported by the article, not claims that we read both works or repeated their experiments.

Nor do these references establish that a particular modern level descends from Karaji's. Similar measurement functions remain comparisons until transmission is documented. We also do not count every chapter, attachment or component as a separate invention: this record joins levelling and alignment procedures around one engineering problem rather than inflating the total.

The manual links measurement to matters affecting users: making the route, maintenance, clearing blockages and handing over the work, rather than describing an object only for display ²⁰. This breadth makes the qanat intelligible as work requiring continuing attention. We have no figures for the population served or costs of a project using a particular instrument.

The study also discusses well and qanat protection zones and different soils, interpreting a connection between technical knowledge and regulation ²¹. We describe that dimension without issuing a legal ruling or making an old distance a current statutory requirement. A historical discussion of taste or water treatment provides no present guarantee that water is safe to drink.

The evidence matters because it gathers parts of a project into a retrievable text: ground description, measurement, excavation, upkeep and handover. The 2020 authors see this as important for construction-management history ²². That is their interpretation, not a claim that every organizing practice began here or the whole world followed this book.

They also compare some water passages with modern hydraulic-head and permeability concepts ²³. Such later readings need limits. We do not turn them into claims that Karaji formulated Darcy's law or possessed germ theory. Historical evidence need not be awarded terminology and results absent from its text to deserve attention.

The answer changes when we distinguish the general system from the particular contribution. Qanats are older; the level heading on 26r attributes a design to the author. We therefore record documented refinement in measurement, not priority over all hydraulic engineering ^{24 2}. A diagram copied centuries later is textual evidence, not dated field-tested hardware.

The study describes the manual among the earliest water books, then offers possible construction-manual priority as the authors' assessment ²⁵. We neither conceal their claim nor make it a final verdict. We also do not repeat its statement that Karaji and al-Razi were contemporaries, which conflicts with the lifespans it supplies. A useful source can contain a defective paragraph without that defect travelling into the museum account.

Readers can open the holding institution's image, examine the diagram letters and compare them with open scholarship without first accepting a priority slogan ^{7 11}. Apparatus inferred from a drawing must remain distinct from apparatus measured in a modern experiment; we have presented no such experiment.

The manual is no substitute for current structural engineering, water testing or safety training. Tunnel collapse, air conditions and well hazards are not school activities. This page provides a space for historical measurement on paper, not an invitation to enter underground works or execute an old description at a working site.

Penn catalogues LJS399 as 49 leaves with 14 diagrams in black/red ink; our 26r image belongs to this later copy ²⁶. We inspected 26r,29r,42r and 45v, reading where legible, not editing the whole text or collating every manuscript. That is the actual reading boundary, not something hidden behind an imposing source title.

The institution's rights statement is “No Copyright – United States.” We display a faithful reproduction of a seventeenth-century two-dimensional diagram, crediting the library without claiming a CC0 release the record does not give ⁷. Research/image files remain outside git. The externally hosted image is neither a photograph of original apparatus nor Karaji's autograph.

The 2020 study uses a modern statue of the author in a Tehran water museum alongside manuscript images ²⁷. We do not use that statue as evidence for his appearance or transfer the statue photograph's rights to the manuscript. Choosing the instrument diagram brings visitors closer to the evidence actually available rather than implying personal knowledge we lack.

“Hidden waters” can sound like a magical promise, but the reported chapters bring together ground observation, instruments, work and maintenance ¹. This is a story about making knowledge discussable and measurable, with limits and errors, not a wand finding water without evidence.

Draw a route on paper, label its start 100 and its end 99.6, and imagine a horizontal distance of 200 metres. The drop is 0.4 metres; divide by 200 to get 0.002, then multiply by 100 to get 0.2%. Write “modern example” above the drawing so the exercise never becomes a number attributed to a manuscript.

Now draw two other routes: one straight but rising, another falling but turning. Which question does a direction map answer, and which does an elevation measurement answer? No water, hole, weights or sharp tools are needed. Do not enter wells or tunnels or taste unknown water. The exercise distinguishes two questions; it does not recreate an underground workshop.

• Extraction of Hidden Waters, Penn LJS399/current catalogue; selected leaves only ²⁸.
• Ataie-Ashtiani and Simmons 2020, full study, figures/references, with limits on modern reinterpretation ²⁹.
• TDV and MacTutor biographies for context, name and uncertainty ^{5 6}.