Dichronauts

Last updated July 05, 2024

Dichronauts is a hard science-fiction novel by Australian author Greg Egan. The novel was published by Night Shade Books on 11 July 2017. It describes a universe with two time dimensions, one of which corresponds to the time perception of the characters while the other influences their space perception, for example by rotations in this directions to be impossible. Hence a symbiosis of two life forms is necessary, so that they can even see in all directions. Furthermore, many fundamental laws of physics are altered crucially: Objects can roll uphill or not fall over any more when oriented suitably. There is negative kinetic energy and a fourth state of matter. Planets are no longer spherical, but hyperbolic and therefore have three separate surfaces. Egan describes these details on his website.^[1]

Plot

In the world of Dichronauts, there are two types of beings living in symbiosis with each other: Walkers, who can only see to the west (or east when turning around), provide mobility, while Siders, leech-like creatures running through their skulls, provide additional sight to the north and south. Every city is in a permanent state of migration to follow the sun's shifting orbit and the narrow habitable zone it creates. The Walker Seth and his Sider Theo from the city of Baharabad at the river Zirona join an expedition to the edge of the habitable zone to map safe routes ahead. They encounter a river with the city of Thanton nearby, in which the Walkers seemed to have used poison against their Siders. Seth talks with Theo about their symbiosis. Previously, his sister Elena got pregnant pushing her Sider Irina to abandon her, leaving her side-blind and with a hole in her head. Theo calls through Thanton in the language of the Siders not audible for Walkers and suspects the presence of Sleepsiders, pushing him to ask Seth about Sleepwalkers. Both agree to return to the expedition, where a vote decides against the return to Baharabad and for more explorations. Soon after, the expedition reaches a cliff without another side or bottom visible and suspects to have reached the end of the world.

Background (literature)

Dichronauts describes the dua situation to Egan's the earlier published Orthogonal trilogy, composed of The Clockwork Rocket (2011), The Eternal Flame (2012),^[2] and The Arrows of Time (2013).^[3] The trilogy is about a universe without any time dimensions at all. In the former, the characters perceive a space dimension as time and in the latter, the characters perceive a time dimension as space.

Background (mathematics and physics)

Mathematically, the difference between our universe and the Dichronauts universe is just a single sign switched in the signature of the metric of flat spacetime. Our universe has signature $(-,+,+,+)$ and the Dichronauts universe has signature $(-,-,+,+)$ . A sign change in the signature can be shown in a simplified way by the restriction to two dimensions. A scalar product with signature $(+,+)$ on $\mathbb {R} ^{2}$ (with the canonical basis) is given by:

\mathbb {R} ^{2}\times \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2},{\begin{pmatrix}x_{1}\\y_{1}\end{pmatrix}}\cdot {\begin{pmatrix}x_{2}\\y_{2}\end{pmatrix}}=x_{1}x_{2}+y_{1}y_{2}

.

A scalar product with signature $(+,-)$ on $\mathbb {R} ^{2}$ (with the canonical basis) is given by:

\mathbb {R} ^{2}\times \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2},{\begin{pmatrix}x_{1}\\y_{1}\end{pmatrix}}\cdot {\begin{pmatrix}x_{2}\\y_{2}\end{pmatrix}}=x_{1}x_{2}-y_{1}y_{2}

.

The vectors $(1,0)$ and $(0,1)$ are orthogonal to each other (meaning their scalar product vanishes) other for both signatures. But given the vector $(2,1)$ , the orthogonal direction is spanned by the vector $(-1,2)$ for the first and $(1,2)$ for the second signature. Only the second signature allows for a vector like $(1,1)$ to be orthogonal to itself. Such vectors describe the propagation of light, for example in this case that one light-year is traveled in one year by definition. In the universe of Dichronauts, this leads to the fact, that not the entire space is filled with light, but that there are two dark cones in opposite directions. Calculations and illustrations of this effect are shown on Greg Egan's website.^[4] An interactive applet about the movement and rotation of objects in the Dichronauts universe is also available there.^[5]

A fundamental change between our universe and the Dichronauts universe can be seen in mechanics, where a ramp will act upon an object resting on it with a force (to counteract gravity, so the object doesn't fall through the ramp) which is orthogonal to the ramp. When considering the combined force of it with gravity, the resulting net force will always pull the object downwards the ramp in our universe, but will pull it up the ramp in the Dichronauts universe when the slope is below diagonal. As a result, there is negative kinetic energy in the Dichronauts universe. Illustrations of this effect are shown on Greg Egan's website.^[6]

In our universe with signature $(-,+,+,+)$ , a planet with radius $r$ is described by the inequality $x^{2}+y^{2}+z^{2}\leq r^{2}$ of a sphere, which is convex, bounded and has a surface with one connected component. In the Dichronauts universe with signature $(-,-,+,+)$ , a planet with radius $r$ is described by the inequality $x^{2}+y^{2}-z^{2}\leq r^{2}$ of a rotating hyperbola, which is concave, non-bounded and has a surface with three connected components. In both cases, the acceleration of gravity is orthogonal to the surface. But not only is "orthogonal" different in both universes, gravity is as well. The Laplace operator is given by $\Delta =\partial _{x}^{2}+\partial _{y}^{2}+\partial _{z}^{2}$ in our universe and $\Delta =\partial _{x}^{2}+\partial _{y}^{2}-\partial _{z}^{2}$ in the Dichronauts universe, which changes the form of the gravitational field given by the Poisson equation (of which the Laplace equation is the special case of no matter). Illustrations of the gravitational field are shown on Greg Egan's website.^[7]

Reception

Publishers Weekly writes that the novel is "impressively bizarre" and that "Egan may have out-Eganed himself with this one".^[8]

Kirkus Reviews writes, that "Egan specializes in inventing seriously strange worlds" and "this one might well be his weirdest yet", but "the problem is, it's counterintuitive, so downright odd that it's impossible to visualize the inhabitants, their surroundings, or what's going on." The symbiosis has "plenty of other issues" and the migration "is not even particularly original", when compared to Inverted World by Christopher Priest.^[9]

Russell Letson writes in the Locus Magazine , to "wind up taking large chunks of Advanced Egan on faith" and to have "found the Orthogonal trilogy and Dichronauts impenetrable", but that "still leaves plenty of Egan to work with."^[10]

A French review by Éric Jentile was published in print in Bifrost, #88 in October 2017.^[11]

Related Research Articles

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field.

<span class="mw-page-title-main">Gradient</span> Multivariate derivative (mathematics)

In vector calculus, the gradient of a scalar-valued differentiable function $of several variables is the vector field whose value at a point gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of . If the gradient of a function is non-zero at a point, the direction of the gradient is the direction in which the function increases most quickly from, and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function may be defined by:$

<span class="mw-page-title-main">Vector field</span> Assignment of a vector to each point in a subset of Euclidean space

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space $. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.$

In mathematics, a unit vector in a normed vector space is a vector of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in $.$

In geometry, a normal is an object that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point.

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space $with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection is also orthonormal, and every orthonormal basis for arises in this fashion.$

In special relativity, a four-vector is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts.

In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed.

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative. A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected.

<span class="mw-page-title-main">Scalar potential</span> When potential energy difference depends only on displacement

In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.

In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as $or) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors$

In mathematics, the signature(v, p, r) of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix g_ab of the metric tensor with respect to a basis. In relativistic physics, v conventionally represents the number of time or virtual dimensions, and p the number of space or physical dimensions. Alternatively, it can be defined as the dimensions of a maximal positive and null subspace. By Sylvester's law of inertia these numbers do not depend on the choice of basis and thus can be used to classify the metric. The signature is often denoted by a pair of integers (v, p) implying r = 0, or as an explicit list of signs of eigenvalues such as (+, −, −, −) or (−, +, +, +) for the signatures (1, 3, 0) and (3, 1, 0), respectively.

In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace $of a vector space equipped with a bilinear form is the set of all vectors in that are orthogonal to every vector in . Informally, it is called the perp, short for perpendicular complement . It is a subspace of .$

The vector projection of a vector $a$ on a nonzero vector $b$ is the orthogonal projection of $a$ onto a straight line parallel to $b$ . The projection of $a$ onto $b$ is often written as $or a ∥ b .$

In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is done through an orthogonal transformation.

In geometry, a three-dimensional space is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are called 3-manifolds. The term may also refer colloquially to a subset of space, a three-dimensional region, a solid figure.

The following are important identities involving derivatives and integrals in vector calculus.

In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space.

<span class="mw-page-title-main">Classical group</span>

In mathematics, the classical groups are defined as the special linear groups over the reals $, the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type . The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups .$

In mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type. Raising and lowering indices are a form of index manipulation in tensor expressions.

References

↑ Greg Egan (2016-05-11). "Dichronauts". Archived from the original on 2023-12-16. Retrieved 2023-12-25.
↑ "Title: The Eternal Flame". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.
↑ "Title: The Arrows of Time". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.
↑ Greg Egan (2016-05-11). "Light and the Dark Cone". Archived from the original on 2023-12-23. Retrieved 2023-12-25.
↑ Greg Egan (2016-05-11). "Interative Dichronauts Space". Archived from the original on 2023-12-23. Retrieved 2023-12-25.
↑ Greg Egan (2016-12-11). "Falling Uphill". Archived from the original on 2023-12-23. Retrieved 2023-12-23.
↑ Greg Egan (2016-12-11). "Gravity and the Shape of the World". Archived from the original on 2023-12-23. Retrieved 2023-12-23.
↑ "Dichronauts by Greg Egan". Publishers Weekly . 2017-06-27. Archived from the original on 2024-01-05. Retrieved 2024-03-12.
↑ "Dichronauts". Kirkus Reviews . 2017-05-01. Archived from the original on 2023-12-26. Retrieved 2023-12-26.
↑ Letson, Russell (2020-08-20). "Russell Letson Reviews Dispersion by Greg Egan". locusmag.com. Retrieved 2024-06-01.
↑ "Title: Dichronauts". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.

External links

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[:21-1] Greg Egan (2016-05-11). "Dichronauts". Archived from the original on 2023-12-16. Retrieved 2023-12-25.

[:02-2] "Title: The Eternal Flame". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.

[:13-3] "Title: The Arrows of Time". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.

[:23-4] Greg Egan (2016-05-11). "Light and the Dark Cone". Archived from the original on 2023-12-23. Retrieved 2023-12-25.

[:22-5] Greg Egan (2016-05-11). "Interative Dichronauts Space". Archived from the original on 2023-12-23. Retrieved 2023-12-25.

[:18-6] Greg Egan (2016-12-11). "Falling Uphill". Archived from the original on 2023-12-23. Retrieved 2023-12-23.

[:19-7] Greg Egan (2016-12-11). "Gravity and the Shape of the World". Archived from the original on 2023-12-23. Retrieved 2023-12-23.

[8] "Dichronauts by Greg Egan". Publishers Weekly . 2017-06-27. Archived from the original on 2024-01-05. Retrieved 2024-03-12.

[:30-9] "Dichronauts". Kirkus Reviews . 2017-05-01. Archived from the original on 2023-12-26. Retrieved 2023-12-26.

[10] Letson, Russell (2020-08-20). "Russell Letson Reviews Dispersion by Greg Egan". locusmag.com. Retrieved 2024-06-01.

[11] "Title: Dichronauts". isfdb.org . Archived from the original on 2023-12-27. Retrieved 2023-12-27.

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v t e Greg Egan
Novels	An Unusual Angle (1983) Quarantine (1992) Permutation City (1994) Distress (1995) Diaspora (1997) Teranesia (1999) Schild's Ladder (2002) Incandescence (2008) Zendegi (2010) Orthogonal The Clockwork Rocket (2011) The Eternal Flame (2012) The Arrows of Time (2013) Dichronauts (2017)
Collections	Axiomatic (1995) Luminous (1998) Dark Integers and Other Stories (2008) Crystal Nights and Other Stories (2009) Oceanic (2009) The Best of Greg Egan (2019)
Short Stories	"Neighbourhood Watch" (1987) "The Cutie" (1989) "The Moral Virologist" (1990) "Axiomatic" (1990) "Learning to Be Me" (1990) "Appropriate Love" (1991) "The Hundred Light-Year Diary" (1992) "Transition Dreams" (1993) "Wang's Carpets" (1995) "Luminous" (1995) "TAP" (1995) "Reasons to Be Cheerful" (1997) "The Planck Dive" (1998) "Oceanic" (1998) "Singleton" (2002) "Induction" (2007) "Dark Integers" (2007) "Lost Continent" (2008) "Crystal Nights" (2008) "Didicosm" (2023)