LL109 Match Day 9 links together algebraic notation, Polish comfort food, global place names, English grammar, modernist campus design, and British TV history. René Descartes’s 1637 La Géométrie helped standardize using a, b, c for knowns and x, y, z for unknowns, launching analytic geometry. Bigos, a sauerkraut‑and‑meat “hunter’s stew,” is celebrated as a national dish of Poland and even immortalized in the epic poem Pan Tadeusz.

The day also touches three different cities named Hamilton (in Bermuda, Ontario, and New Zealand), all honoring different historical figures, not Alexander Hamilton. You’ll see how the English subjunctive hides in everyday phrases like “I wish I were…,” how Illinois Institute of Technology in Chicago became a showcase of Ludwig Mies van der Rohe’s modern architecture, and how London Weekend Television fit into ITV’s split weekday/weekend franchise system.

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Study Notes

Question 1: Letters for unknowns in algebra

While he didn’t invent the idea, the convention in algebra of using late alphabet letters (x,y,z) for unknowns and early letters (a,b,c) for known constants is largely credited to what Frenchman, and specifically his 1637 work La Géométrie?

René Descartes, the French philosopher and mathematician, is credited with popularizing the modern convention of using a, b, c for known quantities and x, y, z for unknowns in algebra, especially through his 1637 treatise La Géométrie, an appendix to Discourse on the Method that helped found analytic (coordinate) geometry.

La Géométrie is a mathematical work published in 1637 as one of three appendices to Descartes’s philosophical Discourse on the Method; it introduced a new way of solving geometric problems by translating them into algebraic equations using what we now call Cartesian coordinates. Earlier, François Viète had already pioneered the systematic use of letters for known and unknown quantities, but he used vowels and consonants; Descartes’s early‑versus‑late‑alphabet scheme is the one that stuck.

Connections

  • From Viète to Descartes: In 1591 François Viète’s In artem analyticem isagoge introduced a consistent symbolic algebra with vowels for unknowns and consonants for knowns, a crucial step toward modern algebraic notation; Descartes later modified this to the now‑standard a, b, c vs. x, y, z system.
  • Typesetters and the rise of x: A popular explanation for why x became the most common unknown is that Descartes’s printer supposedly had more x type blocks available, so he pushed x to be the primary unknown—an anecdote that shows how practical printing constraints can influence mathematical conventions.
  • Everywhere in graphics and games: Cartesian coordinate systems (labeled with x and y, and often z) are the backbone of 2D computer graphics and game engines, where object positions and rotations are computed with x‑ and y‑coordinates on a grid.
  • How kids meet Descartes: Educational platforms like Scratch explicitly teach x–y grids and reference “Cartesian coordinates” when explaining how sprites move around the screen, so many children encounter Descartes’s ideas first through coding games, not math class.
  • Philosophy in pop culture: The same Descartes behind our algebra notation coined “cogito, ergo sum” (“I think, therefore I am”), a line that turns up in everything from Monty Python’s “Bruces’ Philosophers Song” to anime like Ergo Proxy and films such as Blade Runner and other works that question what it means to exist.

Sources

Question 2: Polish hunter’s stew (bigos)

A traditional Polish “hunter’s stew” consisting of sauerkraut, fresh cabbage, and assorted meats such as beef, pork, and kiełbasa, which is cooked slowly at a simmer for several hours and is widely considered the national dish of Poland, is known by what five-letter name?

Bigos is a traditional Polish stew of sauerkraut, fresh cabbage, and assorted meats (commonly pork, beef, bacon, and kielbasa) slowly simmered together for hours, producing a rich, tangy, and smoky dish. It is widely regarded as a national dish of Poland and is frequently described as “hunter’s stew” because older recipes used game meat and preserved ingredients suitable for hunts and winter.

Bigos (pronounced roughly “BEE‑goss”) is a Polish term for this cabbage‑and‑meat stew, often made in huge batches and reheated over several days, which many cooks say improves the flavor. Sauerkraut is finely shredded cabbage preserved by lactic‑acid fermentation, giving it a sour flavor, while kiełbasa is the generic Polish word for sausage, especially the smoked pork sausage exported worldwide as “Polish sausage.”

Connections

  • Food as national symbol: Bigos is often called Poland’s national dish and is explicitly described that way in cultural overviews and culinary histories, emphasizing its role as a symbol of Polish home cooking and hospitality.
  • In the national epic: The “most famous literary monument” to bigos appears in Adam Mickiewicz’s 1834 epic Pan Tadeusz, venerated as Poland’s national epic; the poem includes sensuous lines about the stew’s “wondrous taste” and aroma, showing how a humble dish became high literature.
  • Epic cooking and hunting culture: Historical recipes describe bigos as a hunters’ breakfast cooked in cauldrons over open fires, using whatever game was taken and preserved sauerkraut that traveled well—linking the dish to the forests and noble hunting culture of the old Polish‑Lithuanian Commonwealth.
  • Endless regional variants: Food writers note that there are “as many recipes as cooks” in Poland—some versions emphasize wild mushrooms and game, others smoked sausage and bacon, and some add prunes or apples for sweetness—so restaurant and family bigos can taste surprisingly different.
  • Diaspora and comfort food: Bigos appears frequently in Polish‑diaspora blogs, recipe sites, and community newsletters, often described as ideal winter comfort food and a way to use holiday leftovers, so players might have encountered it in family kitchens or immigrant neighborhoods rather than restaurants.

Sources

Question 3: Three cities called Hamilton

GEOGRAPHY - Municipalities on Great Bermuda, in Ontario, Canada, and on New Zealand’s North Island all share what name, though each is named after a different individual, none of whom was a U.S. Founding Father?

The shared name is Hamilton: Hamilton, Bermuda is named for colonial governor Sir Henry Hamilton; Hamilton, Ontario is named for local landowner and town founder George Hamilton; and Hamilton, New Zealand is named after British naval officer Captain John Fane Charles Hamilton, killed in the 1864 Battle of Gate Pā.

Great Bermuda (also called the Main Island) is the largest island in the British Overseas Territory of Bermuda and contains the capital, the City of Hamilton, which was laid out in the 1790s and incorporated in 1793. A municipality is a city, town, or similar local government unit; here it refers to three urban centers sharing the Hamilton name on three different landmasses.

Connections

  • Not that Hamilton: The question pointedly notes that none of these Hamiltons is a U.S. Founding Father—unlike places such as Hamilton, New York, and Hamilton County, New York, which are named after Alexander Hamilton, first U.S. Treasury Secretary and the subject of the hit musical.
  • Capital of a small island nation: Hamilton, Bermuda is the capital of the British Overseas Territory and a major port on Hamilton Harbour, making it a familiar cruise‑ship and offshore‑finance destination far better known than its namesake governor.
  • Industrial city turned film set: Hamilton, Ontario grew into an industrial and steel‑producing center at the western end of Lake Ontario’s Golden Horseshoe; today it’s also a busy film location that often stands in for U.S. cities in productions like The Incredible Hulk and other movies and series.
  • Colonial legacy and renaming debates: Hamilton, New Zealand sits on land once occupied by Māori settlements such as Kirikiriroa and was named for Captain John Fane Charles Hamilton, who died fighting Māori forces; in 2020 the city removed his statue from Civic Square after requests from Waikato‑Tainui, and there has been public discussion about restoring the Māori name Kirikiriroa.
  • Three very different Hamiltons: Together these cities illustrate how the same colonial naming pattern—honoring governors, land speculators, or military officers—can play out in a small island capital, a Canadian industrial hub, and a New Zealand river city, giving geography questions a historical and political dimension.

Sources

Question 4: The subjunctive mood

In the sentences “I wish I were in love again” and “The rule requires that he be present”, the verbs were and be are examples of what grammatical mood?

Both sentences use the subjunctive mood: “I wish I were in love again” uses the past subjunctive were to express a wish contrary to fact, and “requires that he be present” uses the present (mandative) subjunctive be after a verb of requirement.

Grammatical mood is the category that shows how a verb relates to reality or the speaker’s attitude: the indicative states facts (“He is here”), the imperative gives commands (“Be here”), and the subjunctive expresses wishes, hypotheticals, or necessities (“I wish he were here”; “The rule requires that he be here”). In modern English the subjunctive mostly survives in a few patterns—were for unreal conditions and bare verbs (like be, go) in mandative clauses—so it can be easy to overlook even for fluent speakers.

Connections

  • Songs you already know: Pop culture is full of subjunctive titles: “If I Were a Boy” (Beyoncé) and “If I Were a Rich Man” (Fiddler on the Roof) both use the past subjunctive were to imagine unreal situations—exactly the same structure as “I wish I were…”.
  • Formal rules vs. real usage: Modern guides note that “I wish I was” and “If I was” are common in casual speech, but traditional grammar and many style guides still prefer were in counterfactual clauses, especially in writing and exams—precisely the norm LL is testing.
  • Law and bureaucracy English: The mandative subjunctive (bare verb after verbs like require, insist, recommend) is particularly common in legal and administrative language: “The law requires that he be present,” “It is essential that the contract be signed,” etc., so reading official notices is a good way to see it in the wild.
  • English vs. other languages: Reference works often point out that English uses the subjunctive relatively sparingly compared to languages like Spanish or French, where distinct subjunctive verb forms are ubiquitous in everyday speech, which can surprise English speakers learning those languages.

Sources

Question 5: Illinois Institute of Technology (Illinois)

ART - The university that resulted from the merger of the Armour Institute and the Lewis Institute in 1940 has long been a center for modern architecture in the United States, with many campus buildings designed by long-time head of the architecture school Ludwig Mies van der Rohe. This university is the Institute of Technology in what state?

The school is the Illinois Institute of Technology in the state of Illinois, a private research university in Chicago created in 1940 by merging Armour Institute of Technology and Lewis Institute. Its main Bronzeville campus is renowned for its modernist architecture: Ludwig Mies van der Rohe, who led IIT’s architecture department from 1938, designed the campus master plan and at least 19–20 steel‑and‑glass buildings there, including the celebrated S.R. Crown Hall.

Armour Institute of Technology was founded in the 1890s in Chicago with funding from meat‑packing magnate Philip Danforth Armour, inspired by minister Frank Gunsaulus’s “Million Dollar Sermon” about creating a practical technical school; Lewis Institute was a West Side technical and professional college founded in the 1890s from Allen C. Lewis’s estate. Their 1940 merger formed Illinois Tech, now a STEM‑focused university whose historic main campus is a designated architectural district. Mies van der Rohe, already an internationally known modernist, emigrated from Germany to Chicago in 1938, took over the architecture school, and used IIT’s campus as a laboratory for his “less is more” steel‑and‑glass designs.

Connections

  • A campus of Mies buildings: Preservation and architecture groups note that IIT’s main campus contains nearly twenty buildings by Mies, one of the largest concentrations of his work anywhere, making it a pilgrimage site for architecture students and fans of mid‑century modernism.
  • S.R. Crown Hall as icon: Crown Hall, home to IIT’s College of Architecture, is widely regarded as one of Mies’s masterpieces and has been designated both a Chicago Landmark and a National Historic Landmark; its huge column‑free studio space embodies his structural minimalism.
  • Modernism beyond campus: Mies’s IIT work connects directly to other famous commissions like New York’s Seagram Building and Chicago’s 860–880 Lake Shore Drive, so recognizing his “less is more” aesthetic on this campus helps you spot his influence on corporate towers and glass houses worldwide.
  • From sermon to STEM hub: Illinois Tech’s origin story—Gunsaulus promising that with a million dollars he could build an inclusive technical school, and Armour stepping up—shows how 19th‑century philanthropy and industry shaped the American landscape of engineering and architecture education.

Sources

Question 6: LWT and the “Weekend” franchise

TELEVISION - Among the regional broadcasters that gradually merged over the decades to form the British television network ITV were two London-based franchises. One was Thames (later replaced by Carlton), and the other LWT. What did the “W” in LWT stand for?

In LWT, the “W” stands for “Weekend”: LWT originally meant London Weekend Television, the ITV franchise responsible for broadcasting to London and the Home Counties from Friday evening through the weekend, alongside separate weekday franchises such as Thames and later Carlton.

ITV (Independent Television) began as a network of regional companies, each holding a government‑regulated franchise—a license to supply programming in a specific area and time slot; London was unusual in being split between separate weekday and weekend franchises. London Weekend Television held the London weekend franchise from 1968, while Thames Television (1968–1992) and later Carlton Television held the weekday London franchise; by the early 2000s, these identities were absorbed into a unified ITV London brand even though the licenses remain distinct.

Connections

  • Weekend drama and costume hits: LWT produced some of ITV’s most acclaimed dramas, notably Upstairs, Downstairs, a period series about an Edwardian household’s masters and servants that became a global hit and a template for later shows like Downton Abbey.
  • Poirot on Sunday nights: LWT also produced early series of Agatha Christie’s Poirot with David Suchet and remained credited on later episodes, so many viewers associate LWT’s logo with Sunday‑night mystery drama.
  • Politics and the weekend: The station established Weekend World, a long‑running Sunday lunchtime political program, showing how the “weekend” franchise wasn’t just for light entertainment but also serious current‑affairs coverage.
  • Pop‑entertainment factory: An LWT program list includes massively popular 1980s–90s shows such as Blind Date, Gladiators, Surprise Surprise, and You Bet!—so anyone who watched ITV weekend entertainment in that era was steeped in London Weekend Television output.
  • Nostalgic idents: LWT’s colourful “river” ident and earlier logos, accompanied by distinctive jingles, are now staples of British TV nostalgia websites and YouTube compilations, underscoring how closely many UK viewers associate the brand with the feel of the weekend.

Sources