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Grant @syncingsinking.bsky.social · 30/09/2026

The Nerd function is a homomorphism under multiplication

$Page from Katok's Fuchsian Groups. Corollary 5.2,2. If F is an algebraically closed field, then for any a and b, $A = (\frac{a,b}{F}) \approx M(2,F)$. Let $\iota: A \to A$ be the standard involution of A given by the formula $\iota(x) = \bar{x}$, where $\bar{x}= x_0 - x_1 i - x_2 j - x_3 k$ is called the conjugate of x. Then Trd(x) = $x + \bar{x} = 2x_0$ is called the reduced trace of x, and Nrd(x) = $x\bar{x} = x_0^2 - x_1^2 a - x_2^2 b + x_3^2 ab$ is called the reduced norm of x. Notice that Trd(x) = $Tr(g_x)$ and $Nrd(x)=det(g_x)$, where $g_x = \varphi(x)$ is given by the formula (5.2.4). Obviously Nrd(xy) = Nr(x)Nrd(y), Nrd(1)=1. Theorem 5.2.3. A is a division algebra if and only if Nrd(x)=0 only for x=0.$

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Grant @syncingsinking.bsky.social · 28/09/2026

Pizzaboxxx / The Stove Below

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Grant @syncingsinking.bsky.social · 26/09/2026

Few hundred first downs should run out the clock here right

Score bug of Texas - Tennessee football. #1 Texas (3-0) 20 - 10 #14 Tennessee
Both teams with three timeouts
Texas shown possessing the ball, 1st & 10 at TENN 2,641

Score by quarters
TEX 7 3 3 7 20
TENN 3 0 7 0 10

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Grant @syncingsinking.bsky.social · 21/09/2026

Pro tip: if installing a shelf without a level, run 100 trials of a Galton board. If the distribution returns skewed a statistically significant number of times, your shelf is not level.

Galton board on a shelf. The small ball bearings have descended down the triangular top part and into columns below. The distribution is skewed a little to the right, i.e. the peak is left of center, indicating shelf is not level and grades down to the left

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Grant @syncingsinking.bsky.social · 16/09/2026

Draw this figure every year and forget to take a picture

Chalkboard figure. A 3 by 3 square grid. Three horizontal lines colored yellow and connected at a point on left of the grid. Three vertical lines colored blue and meeting at a point below the grid. Three purple diagonal lines, one bottom left to top right, one top left looping around to middle bottom and right middle, one bottom right looping around to top middle and middle left, meeting bottom left of the grid. Similar green diagonals running top left to bottom right.

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Grant @syncingsinking.bsky.social · 02/09/2026

Was drawing the systoles of the Bolza surface and these two jumped out

A chalkboard drawing of a genus 2 surface with two simple closed curves drawn on it. A pink curve loops from the middle of the left-hand side of the left-hand hole, down around the bottom of the hole, to the middle of the left-hand side of the right-hand hole, then back to where it started on the back side (shown by dotted line) around the top of the left-hand hole. A blue loop does the same starting on the right-hand side of the right-hand hole, up around to the right- hand side of the left-hand hole, then dotted down and back around to the start.

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Grant @syncingsinking.bsky.social · 29/08/2026

Spotted while cutting the grass

Big-ass brown spider, possibly about to have small spiders, hanging out on a green leaf. Strands of web are connected to the leaf.

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Grant @syncingsinking.bsky.social · 28/08/2026

Screenshots that contradict themselves

West Wing screenshot. Leo, Toby, Will and CJ seated in the Oval Office, Josh standing between Will and CJ. The caption reads "the door is closed" but the door is visibly open behind CJ

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Grant @syncingsinking.bsky.social · 23/08/2026

Black to play and mate in 8. Not easy - I'm mainly posting because the optimal line involves Black winning with quadrupled pawns. #chess #puzzles

Chess board from Black's perspective. Black piece locations: King c8; Queen c7; Rooks g4, h8; pawns a6, b7, e4, e5, e6, f4. White piece locations: King h1; Queen c2; Rooks a1, e1; Bishop c6; pawns a2, c3, c5, h2. Colored squares indicate last move was White Bishop from b5 to c6.

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Grant @syncingsinking.bsky.social · 22/08/2026

Black to play and mate in 3. How many different solutions can you find? #chess #puzzles

Chess board from Black's perspective. Black piece locations: King c8; Queen g3; Rook h8; Knights d7, f4; Bishops f3, f8; pawns b6, e6. White piece locations: King g1; Queen f2; Rooks a1, e1; Knight c4; Bishop g2; pawns b4, c3, c7, d4. Colored squares indicate last move was White Queen from c2 to f2.

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Grant @syncingsinking.bsky.social · 12/08/2026

On left: Black to play and mate in 4. But Black erred with Ke6, so On right: White to play and mate in 5. #chess #puzzles

Chess board from Black's perspective. Black piece locations: King f7; Queen c8; Rooks b8, h8; Knight g4; pawns a7, b7, c7, d6, e5, g7. White piece locations: King g1; Queen b4; Rooks a1, f1; Bishop g5; pawns a4, b2, e4, f4, g2. Colored squares indicate last move was White pawn from f2 to f4.

Chess board from White's perspective. White piece locations: King g1; Queen b4; Rooks a1, f1; Bishop g5; pawns a4, b2, e4, f4, g2. Black piece locations: King e6; Queen c8; Rooks b8, h8; Knight g4; pawns a7, b7, c7, d6, e5, g7. Colored squares indicate last move was Black King from f7 to e6.

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Grant @syncingsinking.bsky.social · 04/08/2026

Roses as gifts are cheesy Violets' beauty can be subjective

[17] arXiv:2607.28772 [pdf, other]
Hard unknots are often easy from a different perspective
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Comments: 23 pages, 3 figures
Subjects: Geometric Topology (math.GT)

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Grant @syncingsinking.bsky.social · 30/07/2026

Do the Pyrenees and/orr a subset thereof form a partially ordered set?

Map screenshot showing the Pyreneen mountain named Posets and next to it the Parque Natural de Posets-Maladeta

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Grant @syncingsinking.bsky.social · 26/07/2026

White to play and mate in 7. Tricky but interesting if you have a few minutes. (Reposting to correct an error.) #chess #puzzles

Chess board from White's perspective. White piece locations: King g1; Queen h6; Bishop d3; pawns f2, f6, g2, h5. Black piece locations: King h8; Queen d5; Rook g3; Bishops a3, e6; Knight d4; pawns a6, b5, f5, f7, h7. Colored squares indicate last move was Black Rook from g8 to g3.

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Grant @syncingsinking.bsky.social · 22/07/2026

Whoever's move it is to play and mate in 2. (In my game, Black to play and mate in 2. But if White had not taken the Bishop on g3, White would have had a mate in 2.) #chess #puzzles

Chess board from Black's perspective. Black piece locations: King c8; Queen b7; Rooks g6, h8; pawns a5, b6, c7, g7, h7. White piece locations: King g1, Queen b5, Rooks d1, e1; Bishop d4; pawns a4, b2, c3, g3. Colored squares indicate last move was White pawn hxg3.

Chess board from White's perspective. Black piece locations: King c8; Queen b7; Rooks g6, h8; pawns a5, b6, c7, g7, h7. White piece locations: King g1, Queen b5, Rooks d1, e1; Bishop d4; pawns a4, b2, c3, g3. Colored squares indicate last move was White pawn hxg3.

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