Greg Egan
@gregegansf.bsky.social
SF writer / computer programmer
Latest novel: MORPHOTROPHIC
Latest collection: SLEEP AND THE SOUL
Web site: http://gregegan.net
Also: @[email protected]
Latest novel: MORPHOTROPHIC
Latest collection: SLEEP AND THE SOUL
Web site: http://gregegan.net
Also: @[email protected]
Every parallelepiped that you place around an ellipsoid whose faces are tangent to the ellipsoid at their centres has the same volume for a given ellipsoid: 8 a b c, where a, b and c are the semi-axes of the ellipsoid.
November 6, 2025 at 1:45 PM
Every parallelepiped that you place around an ellipsoid whose faces are tangent to the ellipsoid at their centres has the same volume for a given ellipsoid: 8 a b c, where a, b and c are the semi-axes of the ellipsoid.
Every parallelogram that you draw around an ellipse whose sides are tangent to the ellipse at their midpoints has the same area for a given ellipse: 4 a b, where a and b are the semi-axes of the ellipse.
November 6, 2025 at 1:44 PM
Every parallelogram that you draw around an ellipse whose sides are tangent to the ellipse at their midpoints has the same area for a given ellipse: 4 a b, where a and b are the semi-axes of the ellipse.
The portions of the string where it departs from the hyperbola or the ellipse both lie on cones whose axis is a tangent to the curve at that point, and which make an angle with the tangent that is the same as the adjacent segment of the string.
November 1, 2025 at 1:56 AM
The portions of the string where it departs from the hyperbola or the ellipse both lie on cones whose axis is a tangent to the curve at that point, and which make an angle with the tangent that is the same as the adjacent segment of the string.
Here is a version where the point on the ellipse is held still while the point on the hyperbola is swept along it.
November 1, 2025 at 1:55 AM
Here is a version where the point on the ellipse is held still while the point on the hyperbola is swept along it.
Most people know how to draw an ellipse by pinning two ends of a string to a board and sweeping a pencil around inside the string, keeping it taut.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
October 31, 2025 at 10:53 AM
Most people know how to draw an ellipse by pinning two ends of a string to a board and sweeping a pencil around inside the string, keeping it taut.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
Oh, just a caterpillar that keeps all the husks it shed from its head when it was smaller as a kind of elaborate hat … because why wouldn’t you?
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
October 26, 2025 at 10:39 AM
Oh, just a caterpillar that keeps all the husks it shed from its head when it was smaller as a kind of elaborate hat … because why wouldn’t you?
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
Checking in on my recent ebook sales ... at least someone at Amazon has a sense of humour about what to display when there’s an outage.
October 20, 2025 at 7:26 AM
Checking in on my recent ebook sales ... at least someone at Amazon has a sense of humour about what to display when there’s an outage.
From my novel ZENDEGI (2010). I thought this kind of thing would be in widespread use much more rapidly!
October 19, 2025 at 1:23 PM
From my novel ZENDEGI (2010). I thought this kind of thing would be in widespread use much more rapidly!
Gordon had been lost in the fog of Alzheimer’s, but then a new drug halts the progress of the disease, and a kind of neural pacemaker restores his ability to access memories & skills that seemed to have slipped away forever. But no new cure is perfect.
“Spare Parts for the Mind”
“Spare Parts for the Mind”
October 15, 2025 at 6:01 PM
Gordon had been lost in the fog of Alzheimer’s, but then a new drug halts the progress of the disease, and a kind of neural pacemaker restores his ability to access memories & skills that seemed to have slipped away forever. But no new cure is perfect.
“Spare Parts for the Mind”
“Spare Parts for the Mind”
Yeah, sure Amazon, whatever you say.
October 15, 2025 at 10:32 AM
Yeah, sure Amazon, whatever you say.
MacOS helpfully offers translations:
October 7, 2025 at 8:10 AM
MacOS helpfully offers translations:
Just received author’s copies of this translation of “The Clockwork Rocket” [Book One of the Orthogonal Trilogy] from Explorer Books, a Russian-language publisher in the Netherlands.
Explorer Books: explorerbooks.org/product/cloc...
About the Orthogonal Trilogy:
www.gregegan.net/ORTHOGONAL/O...
Explorer Books: explorerbooks.org/product/cloc...
About the Orthogonal Trilogy:
www.gregegan.net/ORTHOGONAL/O...
October 7, 2025 at 4:54 AM
Just received author’s copies of this translation of “The Clockwork Rocket” [Book One of the Orthogonal Trilogy] from Explorer Books, a Russian-language publisher in the Netherlands.
Explorer Books: explorerbooks.org/product/cloc...
About the Orthogonal Trilogy:
www.gregegan.net/ORTHOGONAL/O...
Explorer Books: explorerbooks.org/product/cloc...
About the Orthogonal Trilogy:
www.gregegan.net/ORTHOGONAL/O...
2025: Hoorah, this *looks* perfect! The chatbots will do all the calculus for us!
2030: Wait ... why did that bridge fall down?
2030: Wait ... why did that bridge fall down?
September 30, 2025 at 5:11 AM
2025: Hoorah, this *looks* perfect! The chatbots will do all the calculus for us!
2030: Wait ... why did that bridge fall down?
2030: Wait ... why did that bridge fall down?
There are some expressions whose asymptotic scaling for R >> M I can guess at a glance.
This was not one of them!
This was not one of them!
![Mathematica input: Assuming[R > 0 && M > 0 && 2 M < R,
FullSimplify[
Series[
Sqrt[2] R ArcTan[(Sqrt[R] - Sqrt[R - 2 M])/Sqrt[2 M]] -
Sqrt[M (R - 2 M)], {M, 0, 2}]]]
Output: (4*M^(3/2))/(3*Sqrt[R]) + O(M)^(5/2)](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nyxiyurvidf33xn5bcsotkvc/bafkreihjdsaew745s4vfod724base56ps6cy4g5zxickrmmvy7lmbgd7by@jpeg)
September 26, 2025 at 11:21 AM
There are some expressions whose asymptotic scaling for R >> M I can guess at a glance.
This was not one of them!
This was not one of them!
“The Center for the Alignment of AI Alignment Centers is the world's first and only institution dedicated to the alignment alignment problem.”
“Subscribe unless you want all humans dead forever.”
alignmentalignment.ai/caaac/blog/e...
(H/T @ mhoye @ mastodon dot social)
“Subscribe unless you want all humans dead forever.”
alignmentalignment.ai/caaac/blog/e...
(H/T @ mhoye @ mastodon dot social)
September 12, 2025 at 5:00 AM
“The Center for the Alignment of AI Alignment Centers is the world's first and only institution dedicated to the alignment alignment problem.”
“Subscribe unless you want all humans dead forever.”
alignmentalignment.ai/caaac/blog/e...
(H/T @ mhoye @ mastodon dot social)
“Subscribe unless you want all humans dead forever.”
alignmentalignment.ai/caaac/blog/e...
(H/T @ mhoye @ mastodon dot social)
Suppose we have a unit square, and we want to find the volumes of two 4-dimensional sets — call them “Opp” and “Adj” — consisting of pairs of points inside the square, such that the line containing both points intersects either two opposite sides of the square (Opp), or two adjacent sides (Adj).
September 10, 2025 at 11:30 AM
Suppose we have a unit square, and we want to find the volumes of two 4-dimensional sets — call them “Opp” and “Adj” — consisting of pairs of points inside the square, such that the line containing both points intersects either two opposite sides of the square (Opp), or two adjacent sides (Adj).
This generalises the 3D Grace-Danielsson inequality
(R-3r)(R+r)≥d^2
to:
(R-nr)(R+(n-2)r)≥d^2
where r, R are the radii of the inner and outer spheres, d is the distance between their centres, and n is the dimension. I proved this was sufficient in 2014, but I couldn’t prove that it was necessary.
(R-3r)(R+r)≥d^2
to:
(R-nr)(R+(n-2)r)≥d^2
where r, R are the radii of the inner and outer spheres, d is the distance between their centres, and n is the dimension. I proved this was sufficient in 2014, but I couldn’t prove that it was necessary.
September 3, 2025 at 10:09 PM
This generalises the 3D Grace-Danielsson inequality
(R-3r)(R+r)≥d^2
to:
(R-nr)(R+(n-2)r)≥d^2
where r, R are the radii of the inner and outer spheres, d is the distance between their centres, and n is the dimension. I proved this was sufficient in 2014, but I couldn’t prove that it was necessary.
(R-3r)(R+r)≥d^2
to:
(R-nr)(R+(n-2)r)≥d^2
where r, R are the radii of the inner and outer spheres, d is the distance between their centres, and n is the dimension. I proved this was sufficient in 2014, but I couldn’t prove that it was necessary.
If you pick two points at random inside a regular dodecahedron and draw the line that contains them, that line can intersect three different kinds of pairs of faces, separated by angles of:
π, arcos(–1/√5), or arcos(1/√5)
π, arcos(–1/√5), or arcos(1/√5)
September 1, 2025 at 10:36 PM
If you pick two points at random inside a regular dodecahedron and draw the line that contains them, that line can intersect three different kinds of pairs of faces, separated by angles of:
π, arcos(–1/√5), or arcos(1/√5)
π, arcos(–1/√5), or arcos(1/√5)
But of course it wouldn’t say this without some very good reasons. Like, starting out with some perfectly sane observations, then deciding that convex hulls in four dimensions are magical corridors that defy all the ordinary rules of, umm, convex hulls in any dimension.
August 26, 2025 at 1:16 PM
But of course it wouldn’t say this without some very good reasons. Like, starting out with some perfectly sane observations, then deciding that convex hulls in four dimensions are magical corridors that defy all the ordinary rules of, umm, convex hulls in any dimension.
OK, this is genuinely hilarious.
August 26, 2025 at 1:01 PM
OK, this is genuinely hilarious.
This chart (taken from that Wikipedia article) for obtaining great circle paths from straight lines is especially evocative!
August 21, 2025 at 11:09 AM
This chart (taken from that Wikipedia article) for obtaining great circle paths from straight lines is especially evocative!
The rakali (Hydromys chrysogaster) is Australia's largest rodent. They eat shellfish, fish and other aquatic animals.
But they've also figured out how to eat toxic cane toads safely. They make an incision into the stomach, then remove and eat the heart and liver.
Cute, or what?
But they've also figured out how to eat toxic cane toads safely. They make an incision into the stomach, then remove and eat the heart and liver.
Cute, or what?
August 15, 2025 at 6:13 AM
The rakali (Hydromys chrysogaster) is Australia's largest rodent. They eat shellfish, fish and other aquatic animals.
But they've also figured out how to eat toxic cane toads safely. They make an incision into the stomach, then remove and eat the heart and liver.
Cute, or what?
But they've also figured out how to eat toxic cane toads safely. They make an incision into the stomach, then remove and eat the heart and liver.
Cute, or what?
“Meschers: Geometry Processing of Impossible Objects”
A graphics and material-modelling tool that can systematically handle impossible objects.
Want your Penrose triangles smoothed into bagels, while retaining their delicious impossibility? Meschers can do that.
H/T @[email protected]
A graphics and material-modelling tool that can systematically handle impossible objects.
Want your Penrose triangles smoothed into bagels, while retaining their delicious impossibility? Meschers can do that.
H/T @[email protected]
August 13, 2025 at 12:31 PM
“Meschers: Geometry Processing of Impossible Objects”
A graphics and material-modelling tool that can systematically handle impossible objects.
Want your Penrose triangles smoothed into bagels, while retaining their delicious impossibility? Meschers can do that.
H/T @[email protected]
A graphics and material-modelling tool that can systematically handle impossible objects.
Want your Penrose triangles smoothed into bagels, while retaining their delicious impossibility? Meschers can do that.
H/T @[email protected]
I often enjoy the Friday Brain Teaser on Radio National Breakfast, but they fluffed it today with their claim that a straight cut slicing a cube into equal halves has a square, rectangle, hexagon or rhombus as “the four possible shapes” of the cut surface.
August 8, 2025 at 5:53 AM
I often enjoy the Friday Brain Teaser on Radio National Breakfast, but they fluffed it today with their claim that a straight cut slicing a cube into equal halves has a square, rectangle, hexagon or rhombus as “the four possible shapes” of the cut surface.