Catacaustics Resultants and Kissing Conics - Greg Egan

"A parabolic mirror will focus light rays arriving parallel to the mirror's axis onto a single point: the focus of the mirror. But what happens more generally when light rays strike curved mirrors with other shapes? If we confine ourselves to two dimensions, we can idealise the mirror as a curve in the plane, and plot out the reflected rays produced by light from a given source. In general, rather than passing through a single point, this family of reflected rays will have a curved “envelope” known as the catacaustic of the mirror curve." 5 out of 5 http://www.gregegan.net/SCIENCE/Catacaustics/Catacaustics.html

The Eternal Flame 1-2 - Greg Egan

In Lightspeed Magazine 28 : "Straining against the harness that held her to the observation bench, Tamara cranked the azimuth wheel of the telescope mount. Each laborious turn of the handle beside her nudged the huge contraption by just one arc-chime, and though she still had strength to spare there was nothing to be gained from it: a governor limited the speed of rotation to prevent excessive torques that might damage the gears. The soft, steady clicking of the wheel, usually a reassuring, meditative sound, drove home the machine’s serene indifference to her impatience. When the telescope was finally pointed in the direction of her last sighting of the Object, she lay flat on the bench and wriggled into place beneath the eyepiece. As she brought the image into focus she was granted as glorious a vision as she could have hoped for: there was nothing to be seen here but the usual mundane star trails. The trails were exactly as Tamara remembered them, so she knew that she hadn’t mis-set the coordinates. Twice now, the Object had escaped the field of view that had framed it just one day earlier. Such elusiveness proved that it was crossing the sky faster than anything she’d seen before. Tamara turned the secondary azimuth wheel until she was rewarded with a small gray smudge of light at the top of the field, then she adjusted the altitude to center it. To the limits of the telescope’s resolving power, the Object was simply a point. Nothing in the cosmos was close enough to the Peerless to reveal its width, but even those orthogonal stars that had remained fixed in the sky for three generations showed color trails at this magnification. To possess a point-like image the Object had to be moving slowly—but the only way a slow-moving body could cross the sky as rapidly as this was by virtue of its proximity." 4 out of 5

The Eternal Flame 1 - Greg Egan

"Carlo scooped up the chosen boy's co and pulled himself along the rope into the front room, a child clutched awkwardly in each free hand. From the box he took two clearstone vials and a syringe. He extruded an extra pair of arms, uncapped the first vial and filled the syringe with its orange powder. When he held the sharp mirrorstone tip to the base of the boy's skull he felt his own body start shuddering in revulsion, but he stared down his urge to take the child in his arms and soothe him, to promise him as much love and protection as he would lavish on any child of his own. He pushed the needle into the skin and searched for the angle that would take it between two plates of bone – he knew the invariant anatomy here was not that different from a vole's – but then the tip suddenly plunged deeper without the drop in resistance he'd been expecting upon finding the narrow corridor of flesh. The child's skull wasn't fully ossified, and his probing had forced the needle right through it. Carlo turned the boy to face him then squeezed the plunger on the syringe. The child's eyes snapped open, but they were sightless, rolling erratically, with flashes of yellow light diffusing all the way through the orbs. The drug itself could only reach a small region of the brain, but those parts it touched were emitting a barrage of meaningless signals that elicited an equally frenzied response much farther afield. Soon the tissue's capacity to make light would be depleted throughout the whole organ. In this state, Carlo believed, there could be no capacity for thought or sensation. When the boy's eyes were still Carlo withdrew the needle. His co's tympanum had been fluttering for a while, and now her humming grew audible. “I'm sorry,” Carlo whispered. “I'm sorry.” He stroked the side of her body with his thumb, but it only made her more agitated. He refilled the syringe with the orange powder, quickly drove the needle through the back of her skull, and watched the light of her nascent mind blaze like a wildfire, then die away." 4 out of 5 http://www.gregegan.net/ORTHOGONAL/E2/EternalFlameExcerpt.html

The Orthogonal Universe - Greg Egan

"What would it be like to live in a universe with four dimensions that were all essentially the same? The universe we inhabit has three dimensions of space and one of time, and though relativity has taught us that there is no absolute notion of time that is shared by everyone, the whole variety of directions in space-time that different people might call “the future” is entirely separate from the set of directions that different people might call “north”. What would be the outcome if that distinction were erased, and there were four dimensions that were all as much alike as “north” and “east”? Such a universe is the setting for a trilogy of novels that I’m writing, with the overall title of Orthogonal. The first volume, The Clockwork Rocket, was published in 2011; the second, The Eternal Flame, has just been released by Night Shade books in the US, and will be out from Gollancz in the UK in October. Since time as such is absent from the Orthogonal universe, a first guess might be that it would resemble a snapshot of the world we see around us at a single moment, albeit a snapshot with four dimensions of space rather than three. Worse, it would be a snapshot with no backstory: no sequence of prior events to organize and enrich the subjects caught in the flash. It would consist of nothing but scattered, isolated objects with no history or duration." 4.5 out of 5 http://fantasybookcritic.blogspot.com.au/2012/09/guest-post-orthogonal-universe-by-greg.html

Orthogonal: Riemannian Quantum Mechanics [Extra] - Greg Egan

"Units Throughout these notes, we've adopted a system where time and distance are measured in identical units. This is the equivalent of setting the speed of light, c, equal to 1 in our own universe (for example, by measuring distances in metres and using the time it takes for light to travel one metre as the corresponding unit of time). In the Riemannian universe, it amounts to choosing units for time such that Pythagoras's Theorem holds true, even when one side of the triangle involves an interval of time rather than space. In the novel Orthogonal, it is found empirically that this is the same as setting the speed of blue light equal to 1. In this section, we will go one step further and choose units for mass and energy such that the “reduced Planck's constant”, ℏ = h/(2π), is equal to 1. Mass and energy are then measured in units with the dimensions of inverse lengths or spatial frequencies — or, equally, inverse times or time frequencies. Our particular choice means that the Planck relationship between frequency ν and energy, E = h ν, becomes E = 2 π ν = ω, where ω is the angular frequency of the wave, and the relationship between spatial frequency κ and momentum is p = 2 π κ = k, where k is the angular spatial frequency. The maximum angular frequency ωm that appears in the Riemannian Scalar Wave equation is then simply equal to the rest mass of the associated particle. Relativistic Energy and Momentum Operators In the non-relativistic quantum mechanics we have discussed so far, we have simply applied the usual Schrödinger equation to the potential energy associated with the force between charged particles, on the basis that non-relativistic classical dynamics in the Riemannian universe is identical to Newtonian mechanics, so long as we treat kinetic energy as positive and choose the sign for the potential energy to be consistent with that. For Riemannian relativistic quantum mechanics, we will need to do things slightly differently. The structure of quantum mechanics in its usual formulation is closely linked to the Hamiltonian form of the corresponding classical mechanics, and in the Riemannian case the momentum conjugate to each coordinate in the Hamiltonian sense is the opposite of the relativistic momentum in the same direction."\ 5 out of 5 http://gregegan.customer.netspace.net.au/ORTHOGONAL/07/QMExtra.html

Girih Animation - Greg Egan

"This animation was created using the same methods as the Girih applet, but as it's been precomputed it's possible to include a finer level of detail than can be generated by the applet in real time." 4.5 out of 5 http://www.gregegan.net/APPLETS/32/GirihAnimation.html

Conic Section Orbits - Greg Egan

http://gregegan.customer.netspace.net.au/SCIENCE/ConicSectionOrbits/ConicSectionOrbits0.png

"The aim of this page is to assemble a variety of simple proofs for the wonderful fact, first proved by Isaac Newton, that the orbits of bodies subject to an inverse-square force are conic sections: ellipses, circles, parabolas, hyperbolas or straight lines.

Although conic sections are defined in the first instance as the curves produced when a plane intersects a cone, these curves have a wealth of well-known properties that characterise them equally well. The idea of this page is to explore the relationship between the inverse-square force law and as many of these properties as possible."


5 out of 5

http://www.gregegan.net/SCIENCE/ConicSectionOrbits/ConicSectionOrbits.html

The Eternal Flame - Greg Egan

"Book Two of the ORTHOGONAL trilogy, THE ETERNAL FLAME, has been scheduled to appear in September/October from Night Shade Books in the US and Gollancz in the UK."


http://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html

Booked! Author The Clockwork Rocket - Greg Egan

"It was only in 1996 that I finally came across Gravitation by Charles Misner, Kip Thorne and John Wheeler. Published in 1973, this 1279-page masterpiece takes all the time it needs to prepare the reader for the subject, spelling out the beautiful geometric principles that underly Einstein’s conception of gravity. In general relativity, the way lengths and angles are measured varies from place to place and time to time, so there needs to be an underlying framework in which these concepts can be defined without simply taking them for granted. That framework is known as differential geometry, and once you learn its concepts and tools, black holes, the expanding universe, and other counterintuitive features of modern science finally become comprehensible. This book gives you the mathematics you need, defined with care, but backs it all the way with physical intuition. I only wish I’d read it twenty years earlier."


3.5 out of 5

http://suvudu.com/2011/09/booked-greg-egan-author-the-clockwork-rocket.html

Locus Roundtable on Greg Egan - Karen Burnham

"Welcome to another single-author focused edition of the Locus Roundtable. This time Greg Egan is in the spotlight, as I egregiously abuse my position by wrangling some very kind individuals into talking about my personal current obsession. Participating in this discussion are Gardner Dozois, whose early championing of Egan’s short fiction helped to make him one of the more influential sf authors of the 1990s; Kathleen Ann Goonan, author of the Nanotech Quartet of stories as well as In War Times and This Shared Dream; Russell Letson, long-time reviewer for Locus; and Paul Graham Raven, owner of Futurismic and short story author."


4 out of 5

http://www.locusmag.com/Roundtable/2012/03/roundtable-on-greg-egan/

Art and power in the age of empire: Greg Egan's society of control - Phillip Drake

"The precise realization of the appearance--the surface, I call it, however three-dimensional--is only the most rudimentary beginning. It is the network of relationships between the subjects, and between the subjects and their setting, that constitutes the challenge for the generation that follows. (1)

* In these lines from Greg Egan's short story, "The Caress" (1990), artist and pharmaceutical empire heir, Andreas Lindhquist theorizes on the future of "Lindhquistism," an art movement dedicated to the recreation of classical paintings in real life. Lindhquist achieves these effects by manipulating bodies, light, and space, but, as the above passage suggests, he envisions a future where artists shape the entire "network of relationships" that circumscribe the subjects of the painting. The idea of controlling whole networks of relationships implies an artist with daunting power, who is capable of extending and influencing the array of relationships that shape the ways we think, live, and relate to objects and individuals in the world: an artists who shapes subjectivity itself. As Egan's short story plays out, Lindhquist succeeds so thoroughly that his artworks transgress the boundaries between performance and real-life experience: life literally copies art."



4 out of 5

http://www.thefreelibrary.com/Art+and+power+in+the+age+of+empire%3A+Greg+Egan's+society+of+control.-a0278950693

Re: The Strangest Numbers in String Theory - Greg Egan

"Re: The Strangest Numbers in String Theory

The article was intriguing, but John Huerta’s thesis with all the details looked a bit scary, or at least the kind of thing I’d need to spend six months on to really understand.

Here’s a naive question. The article seemed to imply that you might be able to construct an interaction Lagrangian between fermions and bosons in Riemannian 4-dimensional space by treating both as quaternions, and just multiplying them in the quaternionic way. But don’t you need a scalar for the Lagrangian?"


5 out of 5

http://golem.ph.utexas.edu/category/2011/08/the_strangest_numbers_in_strin.html

The Clockwork Rocket 1 - Greg Egan

"“But how does that change things?” Yalda wondered. “If I see red light and violet light at the same time . . . then the slower, red light must have left the sun earlier.”

“Right. So how does that affect what you see?”

Yalda struggled to picture it. “Where the sun is in the sky depends on which way the world is facing when the light arrives, not when it left. The red light left earlier, but that makes no difference – we just see whatever reaches us at the time we're looking. So we see all the sun's colours in the same place, not spread out in a trail.”

Vito's rear eyes widened with approval. “That wasn't too difficult, was it?”

Yalda was encouraged, but she was still far from confident that everything made sense. “And the stars? Why are they so different?”

“The stars are really moving,” Vito reminded her. “Not just rising and setting with the turning of the world. Between the time when the red light we're seeing now left a star, and the time when the violet light we're seeing now followed it, the star will have moved far enough for us to see the different colours coming from different directions. When we look at the sun, the violet light and the red light follow the same road, even though the red light begins the journey earlier. When we look at a star, the violet light's coming to us from a different place, along a different path than the red.”

Yalda turned this over in her mind. “If the stars are really moving,” she said, “then why don't we see them move?” The coloured worms were all pinned to the rigid black sky, sharing, but never exceeding, the illusory motion that came from the world's shifting gaze. Why didn't they advance along their own trails, wriggling out of their constellations into fresh new patterns every night?"


4 out of 5

http://www.gregegan.net/ORTHOGONAL/E1/ClockworkRocketExcerpt.html

The Science of the Story An Interview With - Greg Egan

" You are currently in the middle of writing the Orthogonal trilogy. What prompted you to begin such a project and what do you hope to gain from such an endeavor?

A few years ago I started thinking about what it might be like to live in a universe that was different from our own in one very simple but profound way: instead of having a fourth dimension, time, that was set apart from the three dimensions of space, you had four dimensions that were completely interchangeable. In this universe, at the deepest level, "the future" and "the past" would be directions no different from "north" and "south" — and just as those compass points take their meaning from a particular object, the Earth, whose axis could as easily be pointing any way at all in space, in this hypothetical universe "the future" and "the past" would always be the future and past of a particular physical object, such as a cluster of stars and planets, rather than a property of the universe itself.

Of course the instinctive response to this is to say that without time, nothing can change, so nothing can happen — the whole universe will be a kind of frozen snapshot. But that turns out not to be true at all. In such a universe, you can still have a "history" laid out across space that, from the inside, would look very much like the passage of time appears to us.

Now, if you make that one simple change, what follows? What would the physics and the chemistry be like, in this new framework? Before I started writing I put a lot of work into fleshing out those details, so I could predict exactly how light would behave, how matter would behave, and what kinds of technology would or wouldn't be possible. The result is a combination of novelty and consistency that really appeals to me: there are a lot of very strange aspects to this universe, but they're not just an arbitrary collection of weird phenomena, they all flow directly from a single premise. "


4 out of 5

http://www.diamondbookdistributors.com/default.asp?t=1&m=1&c=53&s=656&ai=108976

Crystal Nights - Greg Egan

Seiun award nomination, 2011.


5 out of 5

http://www.sfawardswatch.com/?p=4122

Forget the true shape of the planet: The Anarchic Spaces of Greg Egan’s Distress - Brian Greenspan

"“‘Forget the true shape of the planet’: The Anarchic Spaces of Greg Egan’s Distress,” in Jennifer Rutherford and Barbara Holloway (eds.)"


Unseen.

http://www1.carleton.ca/fass/news/2010-fass-publications-and-awards/

Border Guards - Tomasz Jedrzejowski

"Illustration for Greg Egan's story "Border guards"

Nowa Fantastyka 10/2007"


4 out of 5

Oracle - Greg Egan

Novella

Number of words : 18000
Percent of complex words : 12.1
Average syllables per word : 1.5
Average words per sentence : 19.7


READABILITY INDICES

Fog : 12.7
Flesch : 58.0
Flesch-Kincaid : 10.1

PEOPLE

Robert Stoney

A professor of mathematics.

Peter Quint

A spook, and one of Stoney's captors.

Franza Kafka

Not a Commie, and a writer.

Arthur

Stoney's boyfriend at the time of his trouble.

Mr Wills

A detective at the Manchester CID.

Guy Burgess

A corrupted English spy.

Hermann Weyl

A mathematician.

Chris

A friend at school Stoney was in love with who died of bovine tuberculosis.

Eddington

A physicist.

Hardy

A mathematician.

Newton

A scientist.

Helen

A time travelling multiverse shifting android.

Ealing

A movie director.

Everett

Had a time travel theory that was right.

Feynman

A physicist.

Yang

A physicist.

John Hamilton

Professor of Mediaeval and Renaissance English at Magdalene College, Cambridge. Also an author of religious defenses and children's fantasies.

Elizabeth Anscombe

A philosopher and winner of a debate with Hamilton.

Aquinas to Wittgenstein

Philosophers.

William Hamilton

John's brother.

Malcolm Muggeridge

Another mathematician that did war work.

Nevill Mott

Made the superconducting alloys for the imager.

Rosalind Franklin

From Birkbeck, helped perfect the fabrication process for the computing circuits.

William Blake

A poet.

Joyce Hamilton

John's dying wife.

Helen of Troy

Ancient beauty.

Huysmans

Basically just a very dim Catholic.

Luke

Assistant and an affair of Stoney's.

Wagner

A composer.

Michael Polanyi

An academic philosopher who agrees to moderate the debate.

Kurt Godel

Austrian mathematician.

Aristotle

Ancient philosopher.

Hamilton's young friend

Has a PhD in algebraic geometry from Cambridge.

H.G. Wells

An author.

Milton, Dante, John the Divine

Writers.


PLACES

Sherborne

A public school he went to.

Thames

A river in England.

Westminster Abbey

A church in England.

Saint Paul's Cathedral

A big church in England.

Cavendish Laboratory

Where Stoney works at Cambridge. A mid-Victorian building.

Cairo

City in Egypt.

Bogota

City in Colombia.

London

Capital of England.

Calcutta

City in India.

Manchester

City in England.

Boston

USA city.

Auschwitz

A nazi concentration camp.

Madras

City in India.

Shepherd's Bush

Where the BBC studios are located.

Guy's Hospital

Stoney knows an oncologist there.


ORGANISATIONS

CID

Police detectives.

Trinity College

Part of Cambridge University.

MI6

English international espionage agency.

Socratic Club

A society that holds debates at Oxford University.

BBC

British Broadcasting Corporation.

Oxford University

In England.

Cambridge University

In England.




TECHNOLOGY

Mark I

A computer.

Spin resonance imager

Used to see inside the human body.


MEDIA

Yang and Mills in '54

A paper that generalised Maxwell's equations for electromagnetism to apply to the strong nuclear force.

Physical Review

A physics journal.

Kingdom of Nescia

Children's fantasies by John Hamilton.

Signs and Wonders

Anti-materialism tract by John Hamilton.

The Broken Planet

Anti-science book by John Hamilton.

Faustus

Devil-dealing character.

Letters from a Demon

Satirical newspaper column by John Hamilton.

Cedric Duffy

A John Hamilton character.

Pendragon

Mythical Arthurian leader.

Tower of Babel

Mythical ancient structure.

Mythopoesis

Essay by Tollers.

Can A Machine Think?

A BBC debate between Stoney and Hamilton.

The Seat of Oak

One of Hamilton's Nescia books.


CONCEPTS

Baudot Code

A character set for telegraphy.

Mercury

Roman deity.

Pan

Woodland deity.

Incompleteness Theorem

Postulated by Kurt Godel.

The Goldbach conjecture

One of the oldest unsolved problems in number theory and in all of mathematics. Every even integer greater than 2 can be expressed as the sum of two primes.

Fermat's Last Theorem

About positive integer algebra.

Oracle

A machine that could solve the halting problem.



ANIMALS

Pekinese

A created dog breed.

Hamsters

Small rodents that will fuck anything.


PLOT


Robert Stoney is a professor of mathematics and of interest to MI6 because of the work he could do. He is also exploited by some dodgy spooks because he is gay, and in this decade that is something that can be used against you.

They actually take him to try and torture it out of him at one stage, locking him in a cramped cage. Amazingly, he is rescued by a woman who is a time traveller. Even more than that, an android and a multiversal troubleshooter. Helen stays with him for some time, and they discuss the problems of trying to change the past, and the differing branches. They can't change big things, but certainly can affect minor elements. So they bedevil the spook Quint that tortured Stoney, driving him towards breakdown.

This soon leads him to success as she can point out some shortcuts in research to come up with some technology like a resonance imager, or medical breakthroughs, even if it is not his field.

Others wonder why he is so successful all of a sudden, and he attracks the interest of a religious conservative and anti-science and anti-materialist author John Hamilton. They end up debating on the BBC, which goes ok. Helen accompanies Stoney and Hamilton has a 'young adviser'. Hamilton's wife Joyce is dying of bone cancer, but he thinks Stoney is of the devil and refuses any help.

Something Helen tells John can be accomplished with timeline tricks is a solution to the halting problem, of being able to tell if a computer program will work or not because you can use an infinite number of paths to interrogate it. To be able to solve the halting problem would give you an Oracle machine, as Stoney calls it.

At the end, after his wife has died he is visited by a version of himself from another timeline, which rather freaks him out. He still refuses to accept technological assitance towards his happiness, however and will not go with his visiting self.


4 out of 5

http://www.gregegan.net/MISC/ORACLE/Oracle.html

Hamsters : Oracle - Greg Egan

Small rodents that will fuck anything.


4 out of 5

Pekinese : Oracle - Greg Egan

A created dog breed.


3 out of 5

Oracle : Oracle - Greg Egan

A machine that could solve the halting problem.


4 out of 5

The Goldbach conjecture : Oracle - Greg Egan

One of the oldest unsolved problems in number theory and in all of mathematics. Every even integer greater than 2 can be expressed as the sum of two primes.


3 out of 5

Fermat's Last Theorem : Oracle - Greg Egan

About positive integer algebra.


3 out of 5

Incompleteness Theorem : Oracle - Greg Egan

Postulated by Kurt Godel.


4 out of 5

Pan : Oracle - Greg Egan

Woodland deity.


3 out of 5

Mercury : Oracle - Greg Egan

Roman deity.


3 out of 5

Baudot Code : Oracle - Greg Egan

A character set for telegraphy.


3 out of 5

The Seat of Oak : Oracle - Greg Egan

One of Hamilton's Nescia books.


3.5 out of 5

Can A Machine Think? : Oracle - Greg Egan

A BBC debate between Stoney and Hamilton.


4 out of 5

Mythopoesis : Oracle - Greg Egan

Essay by Tollers.


3.5 out of 5

Tower of Babel : Oracle - Greg Egan

Mythical ancient structure.


3 out of 5

Pendragon : Oracle - Greg Egan

Mythical Arthurian leader.


3 out of 5

Cedric Duffy : Oracle - Greg Egan

A John Hamilton character.


3 out of 5

Letters from a Demon : Oracle - Greg Egan

Satirical newspaper column by John Hamilton.


3.5 out of 5

Faustus : Oracle - Greg Egan

Devil-dealing character.


3 out of 5

The Broken Planet : Oracle - Greg Egan

Anti-science book by John Hamilton.


3 out of 5

Signs and Wonders : Oracle - Greg Egan

Anti-materialism tract by John Hamilton.


3.5 out of 5

Kingdom of Nescia : Oracle - Greg Egan

Children's fantasies by John Hamilton.


4 out of 5

Physical Review : Oracle - Greg Egan

A physics journal.


4 out of 5

Yang and Mills in '54 : Oracle - Greg Egan

A paper that generalised Maxwell's equations for electromagnetism to apply to the strong nuclear force.


4 out of 5

Spin resonance imager : Oracle - Greg Egan

Used to see inside the human body.


4 out of 5

Mark I : Oracle - Greg Egan

A computer.


3 out of 5

Cambridge University : Oracle - Greg Egan

In England.


4 out of 5

Oxford University : Oracle - Greg Egan

In England.


3.5 out of 5

BBC : Oracle - Greg Egan

British Broadcasting Corporation.


4 out of 5

Socratic Club : Oracle - Greg Egan

A society that holds debates at Oxford University.


3.5 out of 5

MI6 : Oracle - Greg Egan

English international espionage agency.


4 out of 5

Trinity College : Oracle - Greg Egan

Part of Cambridge University.


4 out of 5

CID : Oracle - Greg Egan

Police detectives.


3 out of 5

Guy's Hospital : Oracle - Greg Egan

Stoney knows an oncologist there.


3 out of 5