User:Samuel Adrian Antz/Drafts

Hilbert–Lie group
In mathematics, a Hilbert-Lie group is a Hilbert manifold with a compatible group structure, similar to how a Lie group is a smooth manifold with a compatible group structure. Unlike the latter, Hilbert-Lie groups can have infinite dimensions and hence provide a suitable formalism to generalize methods from differential topology for application in functional analysis. Hilbert-Lie groups are named after the German mathematician David Hilbert and the Norwegian mathematician Sophus Lie.

See also

External links
 * Banach–Lie group
 * Fréchet–Lie group
 * Hilbert Lie group on nLab

Hilbert–Lie algebra
In mathematics, a Hilbert–Lie algebra is a Hilbert space equipped with a compatible Lie bracket. Analogous to a Lie algebra being the tangent space of a Lie group, a Hilbert–Lie algebra is the tangent space of a Hilbert–Lie group. Hilbert-Lie algebras are named after the German mathematician David Hilbert and the Norwegian mathematician Sophus Lie.

See also


 * Banach–Lie algebra
 * Fréchet–Lie algebra

External links


 * Hilbert Lie algebra on nLab

Banach–Lie group
In mathematics, a Banach-Lie group is a Banach manifold with a compatible group structure, similar to how a Lie group is a smooth manifold with a compatible group structure. Unlike the latter, Banach-Lie groups can have infinite dimensions and hence provide a suitable formalism to generalize methods from differential topology for application in functional analysis. Banach-Lie groups are named after the Polish mathematician Stefan Banach and the Norwegian mathematician Sophus Lie.

See also


 * Fréchet–Lie group
 * Hilbert–Lie group

External links


 * Banach Lie group on nLab

Banach–Lie algebra
In mathematics, a Banach–Lie algebra is a Banach space equipped with a compatible Lie bracket. Analogous to a Lie algebra being the tangent space of a Lie group, a Banach–Lie algebra is the tangent space of a Banach–Lie group. Banach-Lie algebras are named after the Polish mathematician Stefan Banach and the Norwegian mathematician Sophus Lie.

See also


 * Hilbert–Lie algebra
 * Fréchet–Lie algebra

External links


 * Banach Lie algebra on nLab

Fréchet–Lie group
In mathematics, a Fréchet-Lie group is a Fréchet manifold with a compatible group structure, similar to how a Lie group is a smooth manifold with a compatible group structure. Unlike the latter, Fréchet-Lie groups can have infinite dimensions and hence provide a suitable formalism to generalize methods from differential topology for application in functional analysis. Fréchet-Lie groups are named after the French mathematician Réne Maurice Fréchet and the Norwegian mathematician Sophus Lie.

See also

External links
 * Banach–Lie group
 * Hilbert–Lie group
 * Fréchet Lie group on nLab

Fréchet–Lie algebra
In mathematics, a Fréchet–Lie algebra is a Fréchet space equipped with a compatible Lie bracket. Analogous to a Lie algebra being the tangent space of a Lie group, a Fréchet–Lie algebra is the tangent space of a Fréchet–Lie group. Fréchet-Lie algebras are named after the French mathematician Réne Maurice Fréchet and the Norwegian mathematician Sophus Lie.

See also


 * Hilbert–Lie algebra
 * Fréchet–Lie algebra

External links


 * Fréchet Lie algebra on nLab

Four-dimensional Yang-Mills theory
In mathematical physics, four-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be four. This special case allows for the Yang-Mills equations in second order to be reduced to the simpler (anti) self-dual Yang-Mills equations in first order.

External links


 * self-dual Yang-Mills theory on nLab

Rational homotopy sphere
In algebraic topology, a rational homotopy $$n$$-sphere is an $$n$$-dimensional manifold with the same rational homotopy groups as the $n$-sphere.

Definition

Properties


 * Every (integral) homotopy sphere is a rational homotopy sphere.

Examples

=\mathbb{Z}$$ and $$\pi_1(\R P^n) =\mathbb{Z}_2$$ for $$n>1$$, which vanishes after rationalization. $$\R P^1\cong S^1$$ is the sphere in particular.
 * The $n$-sphere $$S^n$$ itself is obviously a rational homotopy $$n$$-sphere.
 * The Poincaré homology sphere is a rational homology $$3$$-sphere in particular.
 * The real projective space $$\R P^n$$ is a rational homotopy sphere for all $$n>0$$. The fiber bundle $$S^0\rightarrow S^n\rightarrow\mathbb{R}P^n$$ yields that $$\pi_k(\mathbb{R}P^n)\cong\pi_k(S^n)$$ for $$k>1$$ and $$n>0$$ as well as $$\pi_1(\R P^1)

See also


 * Rational homology sphere

External links


 * rational homotopy sphere on nLab

Rational homology sphere
In algebraic topology, a rational homology $$n$$-sphere is an $$n$$-dimensional manifold with the same rational homology groups as the $n$-sphere.

Definition

Properties


 * Every (integral) homology sphere is a rational homology sphere.
 * Every simply connected rational homology $$n$$-sphere with $$n\leq 4$$ is homeomorphic to the $$n$$-sphere.

Examples

\cong\mathbb{Z}$$ \cong\mathbb{Z}\oplus\mathbb{Z}_2$$ \cong 1$$
 * The $n$-sphere $$S^n$$ itself is obviously a rational homology $$n$$-sphere.
 * The pseudocircle (for which a weak homotopy equivalence from the circle exists) is a rational homotopy $$1$$-sphere, which is not a homotopy $$1$$-sphere.
 * The Klein bottle has two dimensions, but has the same rational homology as the $1$-sphere as its (integral) homology groups are given by:
 * $$H_0(K)
 * $$H_1(K)
 * $$H_2(K)


 * Hence it is not a rational homology sphere, but would be if the requirement to be of same dimension was dropped.

\cong\begin{cases} \mathbb{Z} & ;k=0\text{ or }k=n\text{ if odd} \\ \mathbb{Z}_2 & ;k\text{ odd},0<k<n \\ 1 & ;\text{otherwise} \end{cases}.$$
 * The real projective space $$\R P^n$$ is a rational homology sphere for $$n$$ odd as its (integral) homology groups are given by:
 * $$H_k(\R P^n)


 * $$\R P^1\cong S^1$$ is the sphere in particular.


 * The five-dimensional Wu manifold $$W=\operatorname{SU}(3)/\operatorname{SO}(3)$$ is a simply connected rational homology sphere (with non-trivial homology groups $$H_0(W)\cong\mathbb{Z}$$, $$H_2(W)\cong\mathbb{Z}_2$$ und $$H_5(W)\cong\mathbb{Z}$$), which is not a homotopy sphere.

See also


 * Rational homotopy sphere

External links


 * rational homology sphere on nLab

Chaff


"Chaff" is a science-fiction short story by Australian writer Greg Egan, first published in Interzone #78 in December 1993. The short story was included in the collections Our Lady of Chernobyl in 1995, Luminous in 1998 and The Best of Greg Egan in 2019.

Plot

Colombia is stuck in a civil war between five different guerilla organisations. Furthermore a failed terraforming experiment has produced an artifical species known as El Nido occupying a roughly fifty square kilometer large region in the rainforest known as El Nido des Ladrones (Spanish for "the nest of thieves"). After Guillermo Largo vanished into El Nido des Ladrones with classified genetic tools and the appearence of a new drug known as Mother capable to alter bone marrow, the protagonist is sent to capture him alive. Eventually the protagonist finds Guillermo Largo in El Nido des Ladrones and learns about his work on a new drug capable to regenerate synapses and connections in the brain, giving people the possibility to do brain surgery themselves with lobotomy.

Translation

The short story was translated into French (1996 and 2007), Italian (2001) and Spanish (2010).

Reception

Russell Letson, wriitng in the Locus Magazine, claims that the short story "starts with weaponized and monetized biotech, but turns again to matters of moral-psychological choice, both personal and social, as some of that biotech offers a hardened DEA assassin the possibility of remaking his interior moral landscape."

External links

Silver Fire


"Silver Fire" is a science-fiction short story by Australian writer Greg Egan, first published in Interzone #102 in December 1995. The short story was included in the collections Luminous in 1998 and The Best of Greg Egan in 2019.

Plot

Translation

The short story was translated into French (1998), Italian (2001), Japanese (2008) and Spanish (2010).

Reception

Russell Letson, wriitng in the Locus Magazine, states that the short story "is a very strong example of Egan’s interest in matters of disease and morality and his scornful attitude toward irrationality, sentimentality, and ‘'the saccharine poison of spirituality’'."

External links

Zero for Conduct
"Zero for Conduct" is a science-fiction short story by Australian writer Greg Egan, first published in Twelve Tomorrows (a special fiction edition of MIT Technology Review) edited by Stephen Cass in September 2013. The short story was included in the collections The Best of Greg Egan in 2019 and Instantanion in 2020.

Reception

Russell Letson, wriitng in the Locus Magazine, states that the short story is "a very procedural account of how a determined and smart teenaged girl not only devises a breakthrough technology but figures out how to exploit it commercially – all the while navigating a setting that vividly outlines the vulnerabilities resulting from her gender, age, and refugee status."

Salik Shah, writing in the Reactor Magazine, can "imagine that this story could become a film along similar lines to Chiwetel Ejiofor’s The Boy Who Harnessed the Wind (2019, written by William Kamkwamba) or perhaps a storyline set in the larger world of a TV series based on Egan’s novel Zendegi (2010), also set in Iran."

Publishers Weekly writes that "Egan’s talent for creating well-drawn characters shines" in the short story.

External links

The Infinite Assassin


"The Infinite Assassin" is a science-fiction short story by Australian writer Greg Egan, first published in Interzone #48 in June 1991. The short story was included in the collection Axiomatic in 1995.

Plot

Translation

The short story was translated into French (2000), Japanese (2000), Spanish (2001 and 2006) and Italian (2003).

External links

Seeing


"Seeing" is a science-fiction short story by Australian writer Greg Egan,

Plot

XXXX is driven into hospital after a gun shot injured his brain. He suddenly sees his own body from above in a strange Out-of-body experience and has to adapt to this new view of the world.

Translation

The short story was translated into Italian (2003), Spanish (2006), French (2006) and Japanese (2008).

External links

Into Darkness


"Into Darkness" is a science-fiction short story by Australian writer Greg Egan, first published in Asimov's Science Fiction in January 1992. The short story was included in the collections Axiomatic in 1995 and The Best of Greg Egan in 2019.

Plot

A strange wormhole is randomly jumping around on the surface of the Earth, but seems to be drawn to crowded areas. No reason for its sudden appearance is known, but some assume it to be an experiment by aliens from the future to get into the past with both ends of the wormhole accidently collapsing towards their common barycenter in spacetime. The wormhole is composed of two shells, the outer with a radius of one kilometer being called "The Intake" and the inner one with a radius of two hundred meters being called "The Core". Going over "The Intake" forces macroscopic objects like people (with microscopic expections like the flow of blood possible) to only travel further towards "The Core", which allows to leave the wormhole. Every living being inside it during the moment of jump to a new place is killed. Like radioactive nuclei, the duration of the stay of the wormhole at a certain place follows the mathematical law of a half-time of eightteen minutes. The short story follows John Nately, a high-school science teacher, on his eleventh journey from "The Intake" to "The Core", who again risks his life to save that of others.

Translation

The short story was translated into Japnese (2000), Spanish (2002), Italian (2003), Spanish (2006) and French (2006).

Reception

Russell Letson, writing in the Locus Magazine, claims that "the story framework is a tense and effective physical adventure, while at the same time the narrator recognizes the metaphorical properties of the space he is traversing."

Karen Burnham writes in Greg Egan (Masters of Science Fiction), that the short story is "a pure puzzle-solving story."

Literature



External links

Unstable Orbits in the Space of Lies


"Unstable Orbits in the Space of Lies" is a science-fiction short story by Australian writer Greg Egan, first published in Interzone #61 in July 1992. The short story was included in the collections Axiomatic in 1995 and The Best of Greg Egan in 2019.

Plot

Translation

The short story was translated into Japanese (1996), French (1999), Italian (2003) and Spanish (2006).

Reception

Jon Evans, writing in the Reactor Magazine, thinks that the short story "on one level is about strange attractors, but on another, just as compelling, is about belonging and belief and loneliness."

Russell Letson, writing in the Locus Magazine, states that the short story "lies somewhere between a Borgesian fable and an old Galaxy-style comic inferno: a literalized metaphor worked out with science-fictional rigor."

External links

The Kidnapping


"The Kidnapping" is a science-fiction short story by Australian writer Greg Egan, first published in XXXX. The short story was included in the collection Axiomatic in 1995.

Plot

XXXX is contacted by hackers, who hold a digital copy of his wife's brain hostage. Meanwhile her physical self is completely safe. He reflects about giving in.

Translation

The short story was translated into Japanese (1999), Italian (2003), Spanish (2006) and French (2006).

External links

Eugene


"Eugene" is a science-fiction short story by Australian writer Greg Egan, first published in XXXX. The short story was included in the collection Axiomatic in 1995.

Plot

A couple intends to spend a large amount of money to artificially create a perfect child for themselves, which they plan to call Eugene. Both of them give in samples of their DNA. At first the plan seems to fail, but then the conciousness of Eugene initiates contact with the couple and tells them, that his existence is not necessary, when he already achieved so much without it.

Translation

The short story was translated into Italian (2003), Spanish (2006), French (2006) and Japanes (2008).

External links

The Safe-Desposit Box


"The Safe-Desposit Box" is a science-fiction short story by Australian writer Greg Egan, first published in Asimov’s Science Fiction in September 1990. The short story was included in the collection Axiomatic in 1995.

Plot

A man wakes up in a new body every day. In many ways, his life lacks purpose as for example taking care of his body is pointless.

Translation

The short story was translated into German (1992), Portugese (1992), Japanese (1993), Romanian (1995), French (1997), Italian (2003) and Spanish (2006).

Reception

Thomas Christensen, writing on sfbook.com, calls it "probably one of the coolest stories in this collection [Axiomatic]."

External links

The Walk


"The Walk" is a science-fiction short story by Australian writer Greg Egan, first published in Asimov's Science Fiction in December 1992. The short story was included in the collection Axiomatic in 1995.

Plot

A man about to be executed accepts the offer of his executioner to get a neural modification helping him to cope his his approaching death.

Translation

The short story was translated into Italian (2003), Spanish (2006), French (2006) and Japanese (2008).

External links

The Moat


"The Moat" is a science-fiction short story by Australian writer Greg Egan, first published in Aurealis #3 in March 1991. The short story was included in the collection Axiomatic in 1995.

Plot

When the investigation of a crime scene involving rape is continued in the laboratory, the sperm samples collected are found to be invisible to genetic testing. It turns out that the DNA and RNA of the rapist were altered to contain more than the primary nucleobases (adenine, cytosine, guanine, thymine, and uracil). They later talk about how often humans separate themselves into "us" and "them". Now the technology they witnessed might be the first sign of this being carried over into the real world.

Translation

The short story was translated into Romanian (1993), Italian (2003), Spanish (2006), French (2006) and Japanese (2008).

Reception

technovelgy.com calls it an "excellent short story about the ways that people are trying to distance themselves from others in our increasingly small planet."

External links

Closer


"Closer" is a science-fiction short story by Australian writer Greg Egan, first published in Eidolon #9 in Winter 1992. The short story was included in the collection Axiomatic in 1995.

Plot

XXXX and Sian

Translation

The short story was translated into Italian (2003), Spanish (2006), French (2006), Japanese (2006) and Portugese (2011).

Background

The Ndoli Device/jewel also appears in the short stories "Learning to Be Me" (1990) and "Border Guards" (1999) by Greg Egan.

Reception

Russell Letson, writing in the Locus Magazine, states that "Egan does not shrink from looking into any abyss, whether the topic is the authenticity of subjectivity or the genuineness of the most intimate relationships."

External links

Border Guards


"Border Guards" is a science-fiction short story by Australian writer Greg Egan, first published in Interzone 148 in October of 1999.

Plot

In the city of Noether in a 3-toroidal universe, Jamal and Margit play a game of quantum soccer, where the field is replaced by a potential well with infinitely high walls, the ball is replaced by a wave function and the players have to exchange energies between the modes with different frequencies to increase the wave function in the goal of the opposite team. Jamal's team loses the game to Margit's team and they talk afterwards. Jamal, who studies the category of complex representations of Lie groups since Emmy Noether was a pioneer of group theory, only ever had interest to learn and not to discover. Margit, on the other hand, reveals herself to have done so. Jamal at first suspects Margit to actually be Ndoli, the Nigerian neurologist who invented the jewel, a device capable to map a brain and hence eroding the border between life and death, or having worked with him. But Margit reveals to have been behind the discoveries of the new terretories like their universe and to now guard their borders. Jamal convinces all their friends from quantum soccer to help her, so she can finally have time to join them to go swimming in the river.

Translation

The short story was translated into Japanese (2001), Italian (2002), Dutch (2006) and French (2009).

Background

The Ndoli Device/jewel also appears in the short stories "Learning to Be Me" (1990) and "Closer" (1992) by Greg Egan.

Reception

Karen Burnham writes in Greg Egan (Masters of Science Fiction), that the short story "has more to do with humanity’s dislocation in becoming immortal, as well as the lasting effects of trauma."

Literature



External links



Seventh Sight
"Seventh Sight" is a science-fiction short story by Australian writer Greg Egan, first published XXXX. The short story was included in the collection Instantanion in 2019.

Plot

Background

The short story was nominated for the Japanese Seiun Award in 2017. It reached the 31st place in the Reader Poll of the Locus Award in 2015.

Reception

Publishers Weekly writes, that the short story is "unexpectedly gorgeous and humanistic."

External links



==References==

Uncanny Valley
"Uncanny Valley" is a science-fiction short story by Australian writer Greg Egan, first published XXXX. The short story was included in the collections Instantanion in 2019 and The Best of Greg Egan in 2020.

Plot

XXXX

Background

The short story was nominated for the British SF Association Award in 2018 and won the Japanese Seiun Award in 2020.

Reception

Salik Shah, writing in the Reactor Magazine, takes from the short story that "Egan is vocal about the rights of 'sentient' software or AI."

Russell Letson, writing in the Locus Magazine, states that the short story "pairs the imposter/authenticity motif with the issue of the legal personhood of artificial minds in a day-after-tomorrow near-future."

External links


 * Uncanny Valley (full text on tor.com)
 * Uncanny Valley (full text on tor.com)

==References==

Bit Players
"Bit Players" is a science-fiction short story by Australian writer Greg Egan, first published XXXX. The short story was included in the collections Instantanion in 2019 and The Best of Greg Egan in 2020.

Plot

XXXX

Background

The short story was nominated for the Japanese Seiun Award in 2020.

Reception

Russell Letson, writing in the Locus Magazine, claims that the short stories "Bit Players", "3-adica", and "Instantiation" all "outline the technical-legal problems of AI personhood as artificial personalities try to escape the virtual-reality game worlds that they have been programmed into." For "Bit Players", he adds that "is so sloppily worked out that newly generated character Sagreda intuitively knows that the physics can’t be consistent."

External links


 * Bit Players (full text on Egan's website)
 * Vedlejší postavy (Czech translation)
 * Vedlejší postavy (Czech translation)

==References==

3-adica
Russell Letson, writing in the Locus Magazine, claims that the short stories "Bit Players", "3-adica", and "Instantiation" all "outline the technical-legal problems of AI personhood as artificial personalities try to escape the virtual-reality game worlds that they have been programmed into." For "3-adica", he adds that it contains "a game employing a topology based on an exotic number theory", which he "still can’t quite follow, though the bit players do, to their eventual benefit."

Instantanion
Russell Letson, writing in the Locus Magazine, claims that the short stories "Bit Players", "3-adica", and "Instantiation" all "outline the technical-legal problems of AI personhood as artificial personalities try to escape the virtual-reality game worlds that they have been programmed into."

This is Not the Way Home
"This is Not the Way Home" is a science-fiction short story by Australian writer Greg Egan, first published XXXX.

Plot

Background

The short story was nominated for the Japanese Seiun Award in 2021.

Reception

External links



==References==

(Axiomatic collection)

The anthology won the spanish Xatafi-Cyberdark Award in 2007. It reached the 6th and then the 3rd place in the Reader Poll of the Locus Award in 1996 and in 1998.

Cocoon
"Cocoon" is a science-fiction short story by Australian writer Greg Egan, first published XXXX. The short story was included in the collection Luminous in 1998.

Plot

Reception

Reviews

Karen Burnham writes in Greg Egan (Masters of Science Fiction), that the short story is "a straightforward bioethics story" and that it "develops its different arguments and illustrates the politicized nature of all such questions very effectively."

Awards

The short story won a Ditmar Award in 1995. It was nominated for the Hugo Award in 1995 and for the Japanese Seiun Award in 1997. It was shortlisted for the Otherwise Award (formerly James Tiptree Jr Memorial Award) and the Theodore Sturgeon Memorial Award both in 1995. It reached the 4th place in the Reader Poll of the Locus Award in 1995 and won Asimov's Reader Poll.

Literature



External links



==References==

Dust
"Dust" is a science-fiction short story by Australian writer Greg Egan, first published in Asimov's Science Fiction in July 1992. The short story was later included in Egan's novel Permutation City.

Plot

Background

Reception

External links



==References==

Glory
Reception

Rich Horton writes on the SF Site, that the short story "opens with a spectacular hard SF coup", which is "all interesting enough, and well executed, but again it didn't quite ignite my imagination."

Riding the Crocodile
"Riding the Crocodile" is a science-fiction short story by Australian writer Greg Egan, first published in One Million A.D. in December 2005. The short story was included in the collections Dark Integers and Other Stories in 2008 and Oceanic in 2009. The short story is set in the same universe as Egan's novel Incandescence.

Plot

XXXX

Background

Reception

Rich Horton writes on the SF Site, that "the portrayal of the far future posthuman culture is intriguing, and the notion of the Aloof comes off pretty well, but never did I quite care."

External links


 * Riding the Crocodile (full text on Egan's website)
 * Riding the Crocodile (full text on Egan's website)

==References==

Oracle


"Oracle" is a science-fiction short story by Australian writer Greg Egan, first published in Asimov's Science Fiction in July 2002. The short story was included in the collections Oceanic in 2009 and The Best of Greg Egan in 2020. The short story is set in the same universe as Egan's short story Singleton and Egan's novel Schild's Ladder.

Plot

XXXX

Background

Reception

Publishers Weekly writes about the short story, that "Egan can be heavy-handed at times" and that "the character Jack serves as a straw-man version of C.S. Lewis" as well as that "Egan’s talent for creating well-drawn characters shines."

External links


 * Oracle (full text on Egan's website)
 * Oracle (full text on Egan's website)

==References==

Sleep and the Soul (short story)
Reviews

Russell Letson writes in the Locus Magazine, that the short story is "an intriguing piece presented as an alternate history where the Jonbar point is a biological change, not a historical one." He adds that "Egan’s logical working out of the consequences of his central idea is fascinating, and the story is involving."

Our Lady of Chernobyl (collection)
Our Lady of Chernobyl is a collection of four science-fiction short stories by Australian writer Greg Egan, published in XXXX.

Contents• Chaff (1993)

• Beyond the Whistle Test (1989)

• Transition Dreams (1993)

• Our Lady of Chernobyl (1994)Reception External links

Instantiation (collection)
Instantiation is a collection of eleven science-fiction short stories by Australian writer Greg Egan, published in XXXX.

Contents• The Discrete Charm of the Turing Machine (2017)

• Zero For Conduct (2013)

• Uncanny Valley (2017)

• Seventh Sight (2014)

• The Nearest (2018)

• Shadow Flock (2014)

• Bit Players (2014)

• Break My Fall (2014)

• 3-adica (2018)

• The Slipway (2019)

• Instantiation (2019)Reception

Reviews

Russell Letson, writing in the Locus Magazine, claims that the short stories "Bit Players", "3-adica", and "Instantiation" all "outline the technical-legal problems of AI personhood as artificial personalities try to escape the virtual-reality game worlds that they have been programmed into." For "Bit Players", he adds that "is so sloppily worked out that newly generated character Sagreda intuitively knows that the physics can’t be consistent." For "3-adica", he adds that it contains "a game employing a topology based on an exotic number theory", which he "still can’t quite follow, though the bit players do, to their eventual benefit."

External links

Sleep and the Soul (collection)
Sleep and the Soul is a collection of ten science-fiction short stories by Australian writer Greg Egan, published in XXXX.

Contents• You and Whose Army? (2020)

• This is Not the Way Home (2019)

• Zeitgeber (2019)

• Crisis Actors (2022)

• Sleep and the Soul (2021)

• After Zero (2022)

• Dream Factory (2022)

• Light Up the Clouds (2021)

• Night Running (2023)

• Solidity (2022)Reception

Russell Letson writes in the Locus Magazine, to be "struck by how consistent Egan has been in his ethical and social concerns; by his relentless pursuit of philosophical questions; by the sometimes daunting sophistication of his mathematical, topological, and cosmological speculations; and by the surprising ways he turns and re-turns his imagination to those questions. Even after seven volumes of short work (and more than a dozen novels and novellas) these variations on themes never get old."

Letson further writes about the title story in the Locus Magazine, that it is "an intriguing piece presented as an alternate history where the Jonbar point is a biological change, not a historical one." He adds that "Egan’s logical working out of the consequences of his central idea is fascinating, and the story is involving."

External links

Phoresis and Other Journeys
Phoresis and Other Journeys is a collection of three science-fiction short stories by Australian writer Greg Egan, published in XXXX.

Contents

• The Four Thousand, The Eight Hundred (2016), ISBN 978-1-59606-791-2

• Dispersion (2020)

• Phoresis (2018), ISBN 978-1-59606-866-7Reception

The Four Thousand, The Eight Hundred

Publishers Weekly writes that the short story "successfully incorporates hot-button issues of intellectual property rights and government reparations for systematic bigotry into a far-future SF story" and is a "top-notch thought-provoking and suspenseful space opera, with impressively effective worldbuilding given its short length."

Dispersion

Russell Letson writes in the Locus Magazine, that the story "combines motifs from all over Egan territory: the social-ethical drama of people under extreme stress of 'Perihelion Summer' and 'The Four Thousand, the Eight Hundred'; the diseases of Distress, 'Silver Fire', and 'Reasons to Be Cheerful'; and the gnarlier physics-and-math exertions of Schild’s Ladder or Incandescence or the 'Luminous'/'Dark Integers' duo." It "is a cousin to Edwin Abbot’s [sic.] Flatland, on steroids laced with LSD" since the "exotic cosmology is overlaid onto a nearly allegorical portrait of communities occupying overlapping but immiscible spaces, facing the same crisis but failing to come together to deal with." He adds to "return to Egan for" the theme "to know and then to do the right thing; to be effective and moral, no matter the difficulty or discomfort."

Phoresis

Russel Letson writes in the Locus Magazine, that the characters "are gregarious, curious, imaginative, methodical, ingenious, and persistent" as well as that the novella is "intensely procedural" and that "the speculative-engineering side of the novel almost evades the feeling of fiction." He further writes that "drama arises from the social setting" and that "execution demands both vision and sacrifice on the part of those who will not see the work’s end", which makes the novella "strongly reminiscent of Incandescence and 'The Four Thousand, the Eight Hundred'." It is "is the Tower of Babel, but without the hubris and confusion: a parable not of division and failure but of the triumph of ingenuity and selflessness – of hope."

Awards

"The Four Thousand, The Eight Hundred" was a finalist for the Ditmar Award in 2016 and reached the 5th place in the Reader Poll of the Locus Award in 2016.

External links

Perihelion Summer
Plot

Taraxippus, a double system of two black holes with the heavier one having one-tenth the mass of the sun, is discovered using gravitational lensing and observing its Einstein rings. It passes through the Solar System and shifts the orbits of the planets. Earth in particular is thrown onto a more elliptical orbit with roughly ten to fifteen degrees more and less while passing through its perihelion and aphelion. Countries prepare, for example by enclosing entire cities under a glass dome or opening borders for refugees. Matt and his friends build the Mandjet, a boat with a self-sustaining ecosystem to stay off land and potentially head to Antartica. They meet other boats at sea, take people on board if needed and form a flotilla together. Matt hears of a fire in his hometown Perth and heads back to save his parents and sister, who all previously deemed staying at sea to be too unsafe. He arrives one hour after his father died of a heart attack, which was fatal as he previously concealed the necessity for a hospital while the family fleed Perth. He also learns that his mother blames him for it and even for Taraxippus, as he didn't stop talking about it. Matt can bring his mother and sister to the Mandjet successfully, but learns it has been taken over by invaders. Together with his friends, they manage gain control again. Matt is then forgiven by his mother.

Reception

Russell Letson writes in the Locus Magazine, that the novella "is certainly more than 'just a ride': a description of how wrong things can go and how fast, a hard-SF, procedural-didactic treatment that follows its disaster from causes through effects and responses, supported by the meticulously precise observations of processes one expects from this writer." He also adds that the "early chapters also sketch in the range of social and political reactions" and that "the rest of the book unpacks the implications of political pathologies and clima­tological disturbances as populations face or flee the deadly extremes of ice and fire." He further thinks that "Egan always insists on examining and unfold­ing the way the world works and the ways we interact with those operations", that the novella "also models the rational, the possible, the decent, and the humane in its picture, as though reluctant to give in to the most melodramatic options offered by the situation" and that Egan is "modeling both an accelerated version of the future we face and a perhaps-as-unlikely kind of response to it – a rational and humane refusal to give up or give in to survivalist power fantasies and magical thinking."

External links

Dispersion
Plot

Reception

Russell Letson writes in the Locus Magazine, that the story "combines motifs from all over Egan territory: the social-ethical drama of people under extreme stress of 'Perihelion Summer' and 'The Four Thousand, the Eight Hundred'; the diseases of Distress, 'Silver Fire', and 'Reasons to Be Cheerful'; and the gnarlier physics-and-math exertions of Schild’s Ladder or Incandescence or the 'Luminous'/'Dark Integers' duo." It "is a cousin to Edwin Abbot’s [sic.] Flatland, on steroids laced with LSD" since the "exotic cosmology is overlaid onto a nearly allegorical portrait of communities occupying overlapping but immiscible spaces, facing the same crisis but failing to come together to deal with." He adds to "return to Egan for" the theme "to know and then to do the right thing; to be effective and moral, no matter the difficulty or discomfort."

External links

Phoresis
Plot

Reception

Russel Letson writes in the Locus Magazine, that the characters "are gregarious, curious, imaginative, methodical, ingenious, and persistent" as well as that the novella is "intensely procedural" and that "the speculative-engineering side of the novel almost evades the feeling of fiction." He further writes that "drama arises from the social setting" and that "execution demands both vision and sacrifice on the part of those who will not see the work’s end", which makes the novella "strongly reminiscent of Incandescence and 'The Four Thousand, the Eight Hundred'." It is "is the Tower of Babel, but without the hubris and confusion: a parable not of division and failure but of the triumph of ingenuity and selflessness – of hope."

External links

The Four Thousand, the Eight Hundred
Reception

Publishers Weekly writes that the short story "successfully incorporates hot-button issues of intellectual property rights and government reparations for systematic bigotry into a far-future SF story" and is a "top-notch thought-provoking and suspenseful space opera, with impressively effective worldbuilding given its short length."

External links

Sea of Dreams
"Sea of Dreams" (Chinese: 梦之海, Pinyin: mèng zhī hǎi) is a science-fiction short story by Chinese writer Liu Cixin.

Plot

During an ice sculpting festival at the Songhua River, a frozen ice ball arrives from the sky. It initiates contact with the artists, revealing itself to be an alien of ungraspable shape to humans enclosed in the ice ball and calls itself a low-temperature artist. Only one of the works sparks its interest, which is from Yan Dong who froze water on thin membranes to get a unique shape of ice crystals. She hence becomes a colleague and friend of the low-temperature artist, but it only wants to talk about art with her. While the low-temperature artist begins a new creation by lifting frozen blocks out of the oceans into orbit, Yan Dong instead asks questions about physics and raises concerns about human survival. At first, the low-temperature artist answers them, explaining to come from an extremely cold cloud of dark matter in intergalactic space and believing, that only art can be a reason to exist as a highly advanced civilization will eventually reach the end of science making even survival trivial. As Yan Dong continues, the low-temperature artist gets enraged and calls her trivial as well and to just be jealous. After every single ocean has been transported, Yan Dong indeed spends days without eating or drinking to look at the marvelous ring of ice around Earth, naming it Sea of Dreams. After a last exchange, the low-temperature artist leaves forever. Humanity begins a project to launch rockets in space to pull the ice back onto Earth with Yan Dong and others also proposing shooting lasers onto the ice to evaporate and move it. The first meteors to land cause great joy due to finally brining rain again, but further meteors don't fully burn up and crash into cities or swirl up dust, causing a little ice age. Ten years later, eighty percent of the oceans have been restored with the rest having evaporated into space. Humanity also begins a project spanning multiple generations to bring water from Jupiter and Saturn to Earth, even planning to pull Europa into orbit around Earth as a new moon. Yan Dong returns to the Songhua River, where the ice sculpting festival was started again. Exited, the group cuts out the first ie cube from the frozen surface.

Reception

Rachel Cordasco, writing for World Literature Today, says that Liu "carefully contrasts this cosmic creative act with the suffering and destruction that the lack of water causes on Earth."

Nicole Beck, writing in Strange Horizons, thinks that "Yan Dong certainly has guts, as many of Liu's protagonists do." But she adds that "if you're looking for a deeply nuanced portrait of an individual psyche, this is not the place. Liu is writing from his love of science and technology. Characterization is the weakest point of his craft."

The Redemption of Time
"The Redemption of Time" (Chinese: 观想之宙, Pinyin: guānxiǎng zhī zhòu) is a science-fiction novel by Chinese writer Baoshu.

Plot

After the expansion of the death lines and the fall of system DX3906 into a black domain with a reduced speed of light, Yun Tianming and 艾 AA are left alone on planet blue. The Hunter with Cheng Xin and Guan Yifan is still in orbit and can only land in millions of years due to relativistic time dilation. Yuan Tianming tells 艾 AA what happened after his deep frozen brain was intercepted by the Trisolaran fleet.

Based on their study of his brain, the Trisolarans build a system called cloud computing allowing them to lie and almost ruining their entire economy, for which essential information was saved in their brains. Yun Tianming refuses cooperation and is tortured, for example by experiencing cannibalism, which the Trisolarans considered natural, or experiencing decades in his own mind, which he uses to invent countless fairy tales as he did with a girl called Ai Xiaowei in his childhood. 艾 AA remarks he met her again at the United Nations when buying DX3906 and herself to be a clone of Ai Xiaowei. Yun Tianming eventually realizes by a failed suicide to be in a simulation and agrees to help the Trisolarans. He proposes altering scientific results send to Earth during the Deterrence Era to block human progress, but proposes changes, which can be deduced to be nonsense from pure theory alone, in an attempt to doublecross the Trisolarans and warn humanity about their new ability to deceive. He also creates art, including the design of Sophon, for the cultural exchange, which he also uses to hide warnings. None are recognized by humans. Yun Tianming admits to gave given away the best chance, which was saving Cheng Xin from being murdered by Thomas Wade by ordering the Trisolarans to change his vision with the sophons. He explains it the same way as he did for the Trisolarans when Cheng Xin failed as a Swordholder, that it was an act of love. A supernatural entity from the late universe passes by the Trisolaran Fleet. It reveals to him the truth about the Trisolarans, which is their tiny size of a grain of rice, and recruits him for an even larger war against an ancient being called lurker which compactified previous dimensions.

Sixty years later, 艾 AA has died of old age. Yun Tianming digs her a grave and commits suicide, before realizing that the supernatural entity had given him an immortal spirit living on. He enters the pocket universe 647 and meets Sophon, who reveals that the lurker actually tore down spacial dimensions to create time, which has not existed in the original universe. Yun Tianming travels through the universe and destroys helpers of the lurker, including the home world of Singer, who destroyed the Solar System. He gets support by Helena (from the prologue of Death's End), who also met a supernatural entity inside the four-dimensional fragment, and whose immortal spirit lived on after her death. She sacrifices her life to stop the lurker. Cheng Xin and Guan Yifan leave pocket universe 647 and are greeted by Yun Tianming and a new clone of 艾 AA with all her memories. Sophon reveals to Cheng Xin, that the five kilograms she left behind will indeed alter the new universe after the Big Crunch. In this new universe, the Trisolaran system is stable with one small star in orbit around the two larger others and the aliens living there being completely different. Red Coast Base was terminated without result, Shi Qiang dies in the Vietnam War and Cheng Xin is a boy being adopted by Zhang Yuanchao. Sophon visits the reincarnation of Yun Tianming in his appartment in Beijing and due to his incredible genius in the last universe, trusts him with the task of telling the new universe about everything that happened. She calls him Liu Cixin, which is his new name in the new universe. Liu Cixin then begins to write down the story of the last universe, beginning with the title of the first book: "The Three-Body Problem".

Controversy

Due to the circumstances of the novel being written and published, the question about whether the events of the book are part of the canon is not fully clear and often debated among fans, which is further sparked by its controversial reception. Although the novel was published with Liu Cixin's allowance by Chongqing Press in China, which also published all three Remembrance of Earth's Part novels, and is even sold in a package together with them, no statement regarding the events being part of the canon was made by either Liu Cixin or Chongqing Press. Baoshu himself writes in the foreword of the novel, that he makes "no claim" whether the novel "constitutes a part of the Three-Body canon" and that he imagines it "as a dedicated fan's attempt to explain and fill out some of the gaps of in the original trilogy."

Arnold–Kuiper–Massey theorem
The Arnold–Kuiper–Massey theorem (or AKM theorem) includes three connected results in the mathematical area of projective geometry about projective planes and their connection to spheres.

Complex AKM theorem

The first orthogonal group O(1) acts on the complex projective space CP^n by complex conjugation.

Quaternionic AKM theorem

Octonionic AKM theorem

External links


 * Arnold–Kuiper–Massey theorem on nLab

The Wandering Earth 3
Background

Some Fans jokingly refer to the movie as "The Wandering Ear" (流浪耳朵). This is because the official poster for the second movie transformed the last "H" of the english title into the roman numeral "II" and hence some non-offical posters for the third movie transformed the "TH" into "III", which reduces "EARTH" to "EAR". But it is expected that the official poster will instead transform the "E" into the chinese number "三" to also reference Liu Cixin's The Three-Body Problem (三体).

Hold Up The Sky

The Time Migration

published under the original title 时间移民 (Pinyin shíjiān yímín)

2018-04-01

Fire in the Earth

published under the original title 地火 (Pinyin de huǒ)

Contraction

Mirror

published under the original title 镜子 (Pinyin jìngzi)

Ode to Joy

published under the original title XXXX

Full-Spectrum Barrage Jamming

published under the original title 全频带阻塞干扰 (Pinyin quán píndài zǔsè gānrǎo)

Sea of Dreams

published under the original title 梦之海 (Pinyin mèng zhī hǎi)

Cloud of Poems

published under the original title XXXX

After the events of Devourer, it returned to Earth and helped make it hollow to rebuild a world for humanity within. The sun in the center is actually a white hole transporting the light from its corresponding black hole orbiting around another star. Artificial gravity is generated by a faster rotation of Earth, so there is none at the poles. The human Yiyi, the dinosaur Bigtooth and an alien clone of the Chinese poetrist Li Bai are headed to the South Pole to leave the Earth and see the Cloud of Poems. Previously the dinosaurs have made contact with a godlike alien civilization, who look down on literature due to their advanced technology. One of the gods talked with Yiyi and Bigtooth and cloned Li Bai to transfer his conciousness into him to demonstrate this opinion. After Yiyi still disagrees, because it is impossible for an alien to feel and think like a human does, Li Bai then wants to transform the entire Solar System into a storage space and write every poem possible to surely surpass his original version. A fleet of his civilization arrives and also destroys the Devourer with only a few dinosaurs fleeing to Earth. Afterwards the nebula is created, which Yiyi, Bigtooth and Li Bai can see after leaving Earth. Yiyi is now amazed by the technology while Li Bai came to enjoy the poems created, even telling about one concerning his friend Yiyi finding love.

The Thinker

published under the original title 思想者 (Pinyin sīxiǎng zhě)

Invisible Planets
Invisible Planets is a science-fiction anthology composed of thirteen short stories as well as three essays by different Chinese writers, including Chen Qiufan, Xia Jia, Ma Boyong, Hao Jingfang, Tang Fei, Cheng Jingbo and Liu Cixin.

Contents

• "The Year of the Rat" by Chen Qiufan

• "The Fish of Liliang" by Chen Qiufan

• "The Flower of Shazui" by Chen Qiufan

• "A Hundred Ghosts Parade Tonight" by Xia Jia

• "Tontong's Summer" by Xia Jia

• "Night Journey of the Dragon-House" by Xia Jia

• "The City of Silence" by Ma Boyong

• "Invisible Planets" by Hao Jingfang

• "Folding Beijing" by Hao Jingfang

• "Call Girl" by Tang Fei

• "Grave of the Fireflies" by Cheng Jingbo

• "The Circle" by Liu Cixin

• "Taking Care of God" by Liu Cixin

The Year of the Rat

by Chen Qiufan, published under the original title XXXX

The Fish of Lijiang

by Chen Qiufan, published under the original title XXXX

The Flower of Shazui

by Chen Qiufan, published under the original title XXXX

A Hundred Ghosts Parade Tonight

by Xia Jia, published under the original title XXXX

Tontong's Summer

by Xia Jia, published under the original title XXXX

Night Journey of the Dragon-House

by Xia Jia, published under the original title XXXX

The City of Silence

by Ma Boyong, published under the original title XXXX

Invisible Planets

by Hao Jingfang, published under the original title XXXX

Folding Beijing

by Hao Jingfang, published under the original title XXXX

Call Girl

by Tang Fei, published under the original title XXXX

Grave of the Fireflies

by Cheng Jingbo, published under the original title XXXX

The Circle

by Liu Cixin, published under the original title XXXX

Taking Care of God

by Liu Cixin, published under the original title XXXX

Hospital trilogy
Hospital (Chinese: 医院三部曲, Pinyin: yīyuàn sān bù qǔ) is a dystopian science-fiction trilogy by Chinese writer Han Song, composed of the novels Hospital, Exorcism and Dead Souls.

Translation

Michael Berry wrote about translating the Hospital trilogy in The Paris Review on 26 January 2024, claiming that „translating the trilogy has fully consumed, even haunted“ him. He concludes that to think „of the trilogy as a dream, or a nightmare, taking place on a deep subconscious level; it is meant to be experienced more than intellectualized or analyzed.“

External links



Exorcism (en)
Exorcism (Chinese: 驱魔, Pinyin: qūmó) is a dystopian science-fiction novel by Chinese writer Han Song and the second part of the Hospital trilogy (Chinese: 医院三部曲, Pinyin: yīyuàn sān bù qǔ).

Plot

Reception

Exorcism achieved an average rating of 7,1/10 on Douban.

External links


 * Exorcism on Douban (Chinese)
 * Exorcism on Douban (Chinese)
 * Exorcism on Douban (Chinese)

Dead Souls
Dead Souls (Chinese: 亡灵, Pinyin: wánglíng) is a dystopian science-fiction novel by Chinese writer Han Song and the third part of the Hospital trilogy (Chinese: 医院三部曲, Pinyin: yīyuàn sān bù qǔ).

Plot

Reception

Dead Souls achieved an average rating of 8,1/10 on Douban.

External links


 * Dead Souls on Douban (Chinese)

Llarull's theorem
In Riemannian geometry, Llarull's theorem states

The theorem is named after the mathematician Marcelo Llarull, who published it in Mathematische Annalen in 1998.

External links


 * Llarull's theorem on nLab

Geroch conjecture
In Riemannian geometry, the Geroch conjecture states that metrics with positive scalar curvature on tori must be flat.

In two dimensions, where the Gaussian curvature $$K$$ equals the scalar curvature $$\operatorname{scal}$$, the Geroch conjecture is an immediate consequence of the Gauß-Bonnet theorem. Given a metric $$g$$ on the torus $$T^2$$, its vanishing Euler characterstic yields:


 * $$\int_{T^2}K\mathrm{d}\operatorname{vol}_g

=\int_{T^2}\operatorname{scal}_g\mathrm{d}\operatorname{vol}_g =4\pi\chi(T^2)=0.$$

External links


 * Geroch conjecture on nLab

Min-Oo conjecture
In Riemannian geometry, the Min-Oo conjecture states that certain Riemannian manifolds must be isometric to the sphere of same dimension with the standard metric. The conjecture was proposed and named after Maung Min-Oo, who published a wrong proof for it in XXXX. The conjecture is correct in two dimensions, but was disproven by Simon Brendle, Fernando Marques and André Neves in 2010.

The Min-Oo conjecture states, that a compact Riemannian manifold

External links


 * Min-Oo conjecture on nLab