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    Futility Closet

    futilitycloset.com · Publication · on HN since 2009

    Futility Closet collects curious facts, historical oddities, puzzles, and math items, and also runs a podcast.

    Visit blogRSSHN submissions
    HistoryCulture & SocietyMath
    What HN says

    HN commenters call it consistently excellent and recommend it, and link its podcast episodes on topics like Ruth Belville and the Doves Type.

    Stats for nerds
    105HN people shared it
    176linked in comments
    3.3Kstory points
    Apr 2026last shared
    2010people per year2026

    Top posts on HN

    1. 1
      A visual proof that a^2 – b^2 = (a + b)(a – b)
      1 person · 731 points · first shared 2024 · 192 comments on HN
    2. 2
      1/999999999999999999999998999999999999999999999999
      1 person · 446 points · first shared 2015 · 84 comments on HN
    3. 3
      Images Created from Prime Numbers
      2 people · 362 points · first shared 2020 · 122 comments on HN
    4. 4
      Einstein went to his office just so he could walk home with Gödel
      1 person · 275 points · first shared 2024 · 141 comments on HN
    5. 5
      Perfect example of real-life hacking
      1 person · 208 points · first shared 2010 · 41 comments on HN
    6. 6
      Lewis Carroll – computing the day of the week for any given date (1887)
      1 person · 199 points · first shared 2024 · 101 comments on HN
    7. 7
      New Mexico: Psychologists to dress up as wizards when providing expert testimony
      1 person · 115 points · first shared 2024 · 118 comments on HN
    8. 8
      All the Way Down
      1 person · 98 points · first shared 2025 · 49 comments on HN
    9. 9
      Rivers
      1 person · 72 points · first shared 2025 · 8 comments on HN
    10. 10
      Breakdown: on Borwein integrals
      2 people · 71 points · first shared 2018 · 4 comments on HN

    What HN people wrote when they linked it

    • DonHopkinsJul 2025

      Oh, then you will really love and want to fuck the name of the "Wave Function Collapse" algorithm! (Maybe Chuck Tingle will write a book about it.) Also "Extreme Learning Machines", "Reservoir Computing", "Liquid State Machines", and "Crab Computing" (I shit you not)! Don't even get me started on "Moveable Feast Machines".

      [Welcome to Coffee Talk, with Linda Richman. Todays topic: Wave Function Collapse is neither quantum physics, particles, waves, nor collapsing functions. Discuss amongst yourselves, while I am constrained to solve all these Sudoko puzzles. Oh, I am so verklempt!]

      https://news.ycombinator.com/item?id=42749675

      DonHopkins 6 months ago | parent | context | favorite | on: Generating an infinite world with the Wave Functio...

      Ha ha, great comment! You're right, WFC's name just refers to quantum mechanics because it sounds cool, not because the algorithm has anything to do with physics, waves, or collapsing functions (it's more just a constraint based Sudoko solver). But I perceive it more as a playful buzzword for a useful algorithm, and not as maliciously deceptive like Deepak Chopra, who I was just commenting on recently (Quantum was cool until Deepak Chopra ruined it for everybody):

      https://news.ycombinator.com/item?id=42714477

      I do think it's useful combined with other techniques like procedural programming, cellular automata, Voronoi diagrams / jump flooding, noise, etc, to steer the higher and lower level structures. Check out Maxim Gumin's work on…

    • GregBuchholzJul 2017

      Anyone have recommendations for learning about mechanical linkages (books/MOOC/other)? Recently I've been intrigued by things like straight line linkages:

      https://en.wikipedia.org/wiki/Peaucellier%E2%80%93Lipkin_linkage

      ...and the Chebyshev "paradoxical" linkage:

      https://www.futilitycloset.com/2015/01/03/chebyshevs-paradoxical-mechanism/

      ...and of course Kempe's "universality theorem", that there is a linkage that traces any polynomial curve.

      https://arxiv.org/abs/1511.09002

      I recently came across "Planar Linkages Following a Prescribed Motion":

      https://arxiv.org/abs/1502.05623

      ...which looks awesome. Especially intriguing are sentences like:

      "In modern terms, the procedure proposed by Kempe is a parsing algorithm. It takes the defining polynomial of a plane curve as input and realizes arithmetic operations via certain elementary linkages. In this work, we approach the question from a different perspective... ...By encoding motions via polynomials over a noncommutative algebra, we reduce this task to a factorization problem."

      But currently the terminology used is considerably over my head. Anyone know what branches of math you should study to be able to understand things like:

      "...we recall that one can embed SE2 as an open subset of a real projective space. This allows us to introduce a noncommutative algebra K whose multiplication corresponds to the group operation in SE2, hence mimicking the role played by dual quaternions with respect to SE3. A polynomial…

    • karaterobotMay 2021

      Just realized that the "blogs" category in my Feedly has 347 entries in it, and about half of them haven't published in more than 3 months.

      Here are some that are prolific and good:

      https://marginalrevolution.com/

      Marginal Revolution: wide-ranging and prolific blog about economics and culture.

      https://evidenceanecdotal.blogspot.com

      Anecdotal Evidence: well-written personal blog, mostly observations on books.

      https://krebsonsecurity.com/

      Krebs on Security: about information security. It's written for a popular audience, which is about the level at which I understand the subject.

      https://mjtsai.com/blog/

      Michael Tsai: collects quotes from other people about ongoing software-related news.

      https://acquisitiontalk.com

      Acquisition Talk: about weapons system acquisition, government procurement, etc. Something I wanted to follow because it's a huge sector that doesn't get a lot of attention.

      https://www.futilitycloset.com/

      Futility Closet: wunderkammer-style blog with historical miscellany, quotes, puzzles, etc. Also a great podcast.

      https://www.tor.com/tag/jo-walton-reads/

      Jo Walton's Reading List: Not strictly a blog, but it's in my RSS feeds. I like to see what she's reading lately, and sometimes I get good recommendations from her (e.g. KJ Parker).

      https://www.bldgblog.com/

      BLDGBLOG: about design, architecture, etc.

      https://www.thisiscolossal.com/

      Colossal: about art and design.

      https://www.subtraction.com/

      Subtraction: about design

    • neotekJan 2020

      So this probably isn't quite what you're looking for, but my favourite podcast discovery in 2019 was Off Book: The Improvised Musical Podcast.

      Each week Jess McKenna, Zach Reino, and their band are joined by a special guest and together they improvised an entire hour-long musical from scratch without anything prepared ahead of time, including the music.

      It's just utterly remarkable how good and clever and funny it is given it's entirely improvised and off the cuff. In my opinion it's one of the most astonishing demonstrations of human creativity I've ever seen, and it's doubly impressive when you remember they do it every single week and still never run out of ideas.

      http://www.earwolf.com/show/off-book/

      I would also HIGHLY recommend the Futility Closet podcast and website. The podcast is described as "forgotten stories from the pages of history" but it's so much more than that, and so is the website. Anyone who enjoys logic puzzles, mathematics, chess, history, old books, and interesting stories will love it.

      https://futilitycloset.com

      https://futilitycloset.com/podcast/

    • quuxplusoneJan 2025

      Here's a previous HN submission about finding Waldo in pi (spoiler: only by cheating significantly re what counts as "Waldo"): https://news.ycombinator.com/item?id=30872676

      I googled around trying to figure out what year James McKee created the Trinity Hall prime. The internet is (IMO) presenting it mainly as some kind of Wonder of the Ancient World — with the date of creation conveniently filed off. The first post below claims that the year McKee left Cambridge and created the prime was 1996. It seems to have hit peak internet presence only in the 2010s, though, so I wish there were an authoritative source to confirm (or deny) the 1996 date.

      https://www.bradyharanblog.com/blog/artistic-prime-numbers

      https://www.futilitycloset.com/2017/09/10/trinity-hall-prime/

      https://www.futilitycloset.com/2020/01/12/more-prime-images/

    • KK7NILNov 2024

      > Computationally it's trivial to detect illegal moves

      You're strictly correct, but the rules for chess are infamously hard to implement (as anyone who's tried to write a chess program will know), leading to minor bugs in a lot of chess programs.

      For example, there's this old myth about vertical castling being allowed due to ambiguity in the ruleset: https://www.futilitycloset.com/2009/12/11/outside-the-box/ (Probably not historically accurate).

      If you move beyond legal positions into who wins when one side flags, the rules state that the other side should be awarded a victory if checkmate was possible with any legal sequence of moves. This is so hard to check that no chess program tries to implement it, instead using simpler rules to achieve a very similar but slightly more conservative result.

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