Ken's blog

the point at coordinates (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24) in 24-dimensional space is ...

in the following chess position (FEN), white has 44 possible moves that get out of check: r6K/QPPPPPPB/NNNNNNNN/8/8/8/8/7k w - - 0 1 is ...

start with a set of consecutive primes.  compute all pairs positive differences among the set, and count the number of times each difference...

the integer sequence 3*2^n fits nicely between the gaps between powers of 2. the sequence 5*2^n fits nicely in the largest gaps (on log sc...

at the end of a season, determine the pitchers and batters who are good by some statistic (in opposing ways) and compile a highlight reel of...

is not the most right way to pronounce world chess champion "Max Euwe", but neither is it the most wrong: "Max You". ...

set yourself up with a mortgage and mouths to feed, so that you may do the horrible thing that you want to do . (expanding from "yuppie...

60/37 = 1.621621 is a good approximation to phi, the golden ratio, and 60 and 37 are nicely relatively prime.  below are multiples of 37 mod...

consider a brick in N dimensions composed of unit hypercubes.  for example, let N=3.  each unit cube is labeled 0 or 1, subject to the follo...

chess variant: ranged pieces can travel through pawns of their own color. 1.Rxa7, etc. become valid opening moves, perhaps problematic. ...

are there any languages written with an alphabet which has at least one distinct letter per phoneme? maybe Thai or Korean (Hangul) . by ...

consider the axis-aligned square between (0,0) and (4,4).  we will draw a binary tree inside this box. the root node is centered on the top ...

a square (or rectangle) fundamental polygon is good for 2D games. previously on the various spaces (manifolds) that a fundamental polygon c...

Prey (2022) presented a neat concept.  fanfic, attempting to improve (despite not having watched the movie): backstories, not sure what or...

transposition table is the other elegant improvement to minimax (after alpha-beta): elegant in principle, hairy to implement in practice. ...

among animals that play, how much less play do the adults do than the young?  (how to quantify amount of play?)  how does the seemingly dram...

on a modern computer, Pari/GP can usually factor RSA-style numbers (the worst case for factoring) of 60 digits (199 bits) in 30 seconds or l...

"Convex Regular Faced" is usually applied to polytopes in 4D and above, but it is a useful term for 3D as well, subsuming the Plat...

phobia: irrational fear of the unfamiliar. philia: irrational lack of fear of the familiar.  (this definition is a bit of a stretch.) wh...

variations on the classic artificial intelligence task of mimicking a specific human (the Target) while being questioned by an Interrogator:...

both people lying on their side, next to each other.  4 possibilities: big spoon, little spoon, face to face, back to back.  we do not count...

previously, a commutative ring with reduction polynomial i^3+1 .  this time, the polynomial (i^4-1)/(i-1) = i^3 + i^2 + i + 1 because of its...

minimum spanning tree, Delaunay triangulation, traveling salesman path, traveling salesman circuit, Euclidean Steiner tree. on a plane, sphe...

"when in doubt, launch nukes.  your superiors will deal with the fallout." (scenario (but not the pun) depicted in the 1964 movie ...

quote heard elsewhere. not knowing anything, an employer is willing to pay a job applicant a maximum of X wage to hire them, for a job tha...

10/day = 0.42 / hour 100/week = 0.60 / hour 100/month = 0.14 / hour 1000/year = 0.11 / hour powers of 10 are easy to scale to your act...

isotropy in chess piece movement is elegant, but because armies start on opposite sides and pawns can't move backwards, forward and bac...

roll some dice, order them by some metric independent of what number the die shows, then read off the numbers in that order. example dice ...

Bernoulli numbers are mysterious, showing up in lots of places, e.g., the zeta function , the gamma function , sums of powers (Faulhaber...

0 K = -273.15 C 10^-12 K = -273.149999999999 C 10^-11 K = -273.14999999999 C 10^-10 K = -273.1499999999 C 10^-9 K = -273.149999999 C...

degrees missing from being flat at vertex: tetrahedron 180 octahedron 120 cube 90 icosahedron 60 dodecahedron 36 (angle defect)*(n...

6 = (6/2)*2 90-degree rotations through a face 3 = 6/2 180-degree rotations through a face 8 = (8/2)*2 120 degree-rotations through a ve...

present a 4D maze as an array of 2D slices.   navigate among cells in a slice with the keyboard arrow keys with the right hand.  navigate am...

project a dodecahedron onto the celestial sphere, then present each of the 12 faces as star chart images for a monthly calendar.  the images...

below are some numbers N with many divisors and for which N-1 and N+1 are both prime, i.e., twin primes. the suffix A indicates a highly c...

knight is the only orthodox chess piece which must change square color every move (parity).  in fairy chess, wazir is another. for normal mo...

zebra or (3,2) leaper is a fairy chess piece that jumps from (0,0) to (3,2) (and 7 other squares by symmetry). below are the minimum numbe...

some fairy chess pieces whose movement is a proper subset of queen moves: ferz wazir commoner (ferz + wazir compound) bishop bishop + ...

we propose chess variants based on correcting "nits" of orthodox chess, things that had made orthodox chess inelegant and complica...

golden ratio: phi = (1 + sqrt(5)) / 2 the version of Binet's formula for the nth Fibonacci number which uses the round-to-the-neares...

proposal for a Haskell language extension: when importing a function from another module, one may optionally also specify a type signature f...

"no good can come of a game of Bad Idea, Worse Idea." (tautologically.)

when not obliterating planets, which was most of the time, the Death Star emitter dish was used as a radio telescope by astronomers on board...

let (relativistic kinetic energy) = (relativistic mass-energy) - (rest mass-energy) (rest mass-energy) = m * c^2 let resq = "remain...

if we hypothesize that the 21 cm hydrogen line is produced by a half-wave dipole emitter, then this predicts that the hydrogen atom is 10.5 ...

linear scale factor of the Mercator projection is sec(latitude).  area scale factor is the square of that. U.S. lower 48 states extends fr...

now that Peter Jackson has established that New Zealand is Middle Earth, go on a real-life quest to dispose of a replica One Ring into some ...

connect 8 cubical rooms in tesseract topology, for a 3D game.  when using a door, you see at most two rooms at a time, so you never directly...