Linear algebra is typically explained using matrices. But matrix theory is just one possible perspective. Below, I describe an alternative approach to linear algebra. Tadeusz Banachiewicz (1882–1954), a Polish astronomer living in Krakow, was passionate about calculating machines. From the 1920s, Banachiewicz developed a method for computations on tables of numbers, which was particularly easy [ ]
Taxi is a cooperative game for players who are familiar with the same city. The goal of the game is to connect selected city streets with a route. Players take turns naming streets that belong to this route. Players rely solely on their memory, meaning they cannot look at a city map. When the streets [ ]
Orinoko is a connection game. It is a cooperative game. It is a family game. You can cheat a bit in it. Count the triangles in the upper and lower tiles in the last picture to see what I mean ;-). I invented Orinoko with my son. Both my son, his friends, and the adults [ ]
If you do not know Stephan Steinbach’s blog Alternative Transport, check it out. Among subjects that interest me, Stephan covers data visualization. At one time, a picture from his post on lexical distance among languages of Europe went viral. Since then, he has been pondering ways to improve the illustration by including more languages, positioning [ ]
I was unable to find a simple and efficient implementation of PageRank. As a consequence, I wrote this post and my own Python code that within ten seconds can compute the PageRank of the Polish Wikipedia containing 17,880,897 links between 1,113,939 articles. For the curious, here are the top ten articles. Title of the article [ ]
Stróż pchnął kość w quiz gędźb vel fax myjń. As far as I can tell, you have just read the first perfect pangram ever made from Polish words with the letters q, v, and x that live on the outskirts of Polish spelling. You can get eleven similar pangrams by permuting the words {kość, quiz, [ ]
In typical Polish crosswords, only nouns in their base form are allowed. These are the only four 7 × 7 squares whose rows and columns are Polish common nouns: C E R A M I K E F E M E R A R E K E T E R A M E J/B O Z A [ ]
1. Zbłaźń mżystość ględów hiperfunkcją. 2. Napełńmyż fuksją tchórzliwość gędźb. 3. Pół figlując, krzywdźże smętność hańb. 4. Wzbudźże frygijką półsmętność chlań. 5. Znałem już pysk świń, chęć flot bądź gór. 6. Pójdźmyż haftnąć z wklęsłości guberń. 7. Mąć, schyl, traf, zgłęb, [ożeń, wódź, (kuś, pnij) (kup, śnij)] [żeń, (odkup, śnij, wóź) (kpij, unoś, wódź)]. Tools [ ]
Inspired by the article “Vector models and Russian literature”, I wrote a program that paraphrases Polish texts. Tools used: fastText word vectors pre-trained on Polish Wikipedia by Facebook Research as a thesaurus, Gensim for retrieving similar words, and PoliMorf, a Polish morphological dictionary for filtering the suggestions. Here are assorted fragments of Polish texts after [ ]
I have recently enhanced the chess search engine I write in my spare time with double-check detection. To test it, I made the engine ingest 5.82 million unique over-the-board games from the 15 Million chess games database kept up to date until 2015. 0.85% of these games turned out to contain double checks. More precisely, [ ]