Ken's blog

e.g., accidentally set the number of dimensions in the universe to not an integer. ...to not a real number. previously, gods stupidly at...

below are the 129 primes less than 27^2 = 729, written in big-endian base 27, using the following straightforward encoding of base-27 digits...

model a real scalar field oscillating in space and time as a sum of cosines: f(t,x,y,z) = sum over i of a[i]*cos(b[i] + c[i]*t + d[i]*x + ...

pick one of the many methods for placing N "equally spaced" points on a sphere (e.g., Thomson problem, Tammes problem), compute th...

suit major, rank major (2 possibilities) ordering of suits (4! = 24) king high, ace high (2) low instead of high (i.e., reverse the ra...

we rearrange the standard triple-angle trigonometric identity for sine to make it more clear the cubic polynomial that you need to solve for...

odd numbers have multiplicative inverses modulo 2^n (even numbers do not). ? for(n=1, 8, print1(2^n,":"); for(j=1, 2^(n-1), i=2*j...

inspired by "___: the 3D virtual reality experience"

in base 2, the battle between pi and 2pi (tau) is over where to put the decimal point: 1.10010010000111111011010... = pi/2 11.001001000...

is the 21 cm (1420 MHz) hydrogen line the easiest radio astronomy "target"?  not really a target if observing the hydrogen radiati...

we propose a Haskell syntax extension which may be useful when a record type has very few data values of that type, perhaps just one, e.g., ...

permitting up to two ledger lines above or below, there are 19 possible note positions on a 5-line musical staff. consider adding these 19...

2 closely related chess variants: pawn promotion (pawn reaching 8th rank) causes immediate victory. if a pawn promotes, it must immediately ...

a cube can be oriented in 24 ways (octahedral group, isometries of a cube) .  vote two letters off the island, then mark a cube with 24 lett...

see those sheep over there in that pasture?  I sexually pleasured all of them.  (various details about doing a good job at it, how the sheep...

4 consecutive primes as near to each other as they can possibly be is called a prime 4-tuplet or prime quadruplet or prime decade because, f...

almost all the characters in the movie are male, suggesting its fictional universe has very few females.  so, at the end, when the protagoni...

in polar coordinates, r = a + cos(b*(theta+pi/2)/c) defines a family of pretty curves bounded by a circle, vaguely similar to Lissajous ...

"it slices!  it dices!  it circumcises!  the Person Name Memorial Turbo Encabulator is the kitchen tool you cannot live without!  why ...

define the ranged pieces queen, rook, and bishop to be female. define the non-ranged pieces king, knight, and pawn to be male. but I can...

apply neural network machine learning on positions of a theoretically drawn but hard to defend chess endgame such as KRBKR.  can an AI playi...

little-endian radix conversion and unconversion in Pari/GP: tobase(n,x)= my(l=List); while(x>0, my(r=x%n); listput(l,r); x-=r; x/=n); l...

the following Perl script feeding GP uses Lagrange polynomials to interpolate a polynomial between given points.  input is stdin (or a file ...

Eris tosses a golden apple among Hera, Athena, and Aphrodite, and they immediately start fighting over it, causing the typical amounts of de...

"...I'd buy you various expensive goods." that's sweet. "...I'd buy your love." well, that turned dark. ...

team A rises to power and nearly genocides ("humanitarian crisises") team B.  team B survivors regroup, play the plucky underdogs ...

we set up some common chess openings, direct one side to play the worst moves according to MultiPV of the Stockfish chess engine and the oth...

running one lap around the track in 4 minutes is just like running a 4-minute mile, except you only have to go around the track once.

derivatives are easy; integrals are hard: "most" functions can be differentiated in closed form, but "most" functions do...

102 = 17*6 and 221 = 13*17 have low digit weight, so it is easy to add or subtract those multiples of 17 and 13 without many carries. 17*1...

order the objects in the solar system by decreasing mass.  what is the mass of object number N, where N is human population (currently 8.2 b...

the numbers output by the following Perl script are easy to mentally multiply by any 1-digit number 0 1 2 3 4 5 6 7 8 9: perl -lwe '$c...

an order N+1 Hilbert curve concatenates 4 copies of order N.  therefore, one can draw an order N curve, then seamlessly continue the curve i...

fly anywhere, unimpeded by the rods.  you can see quite far because the rods are thin.  slide a cursor that rides on the rods to the exit. ...

at first glance, a giant gun seems not a very practical method for space launch, because very few payloads, certainly not humans, can surviv...

if you quit with Q instead of q (which is possible to do by accident, e.g., CAPS LOCK accidentally on), mpv stores its resume or "watch...

a multiplication table between pairs of small prime numbers: * 13 17 19 23 29 31 37 41 ...

consider a horizontal row of dots equally spaced 1 unit apart.  put another such row above it, also with horizontal spacings of 1 unit.  let...

consider the vertices of a regular n-gon with side length 1, centered on the origin and an additional "inner" point at Cartesian c...

concentrically inscribe a regular M-gon inside a regular N-gon.  rotate their relative orientation and reinscribe, adjusting the size of onl...

what major conflicts had 3 main parties? a Scotsman, Irishman, and Englishman walk into a bar. they drink all the alcohol. (a country th...

solutions to the Thomson problem up to 12 points (excluding 11) have nice symmetry.  (though I feel that the solution for 1 point also lacks...

{0, 1, 2} are special.  find or create (interesting) theorems that are true precisely for each of the 8 possible subsets of those numbers un...

first, here are integers from -20 to 100.  to negate a balanced ternary number, swap + and -, leave 0 unchanged. -+-+ -20 -+0- -19 -+00...