# Which shape for an infinite world with usual sun cycles?

In fantasy works, it can be interesting to imagine an infinite world. It means you can travel in any direction for as long as you want, always discovering new lands, new cultures, new landscape, etc.

By infinite world, I mean an infinite habitable surface.

However how should such a world be shaped to have a "normal" sun cycle ? That means to have the following features (which the Earth actually have) :

• The sun travels through the sky and when the night comes it disappear behind the horizon.
• There are places on Earth with seasons. For simplicity, assume it only means longer days with the sun higher in the sky during some periods (summer) and shorter days with the sun lower in the sky during others (winter).
• There are places on Earth without seasons.
• The world looks locally flat (there can be geological stuff, like mountains, but no obvious curvature of the world at short scale).
• The fraction of the world which is habitable is infinite.

Note that since it is a fantasy question, the world can

• Have a different sun every day.
• Some part of the world can have behaviour not known on Earth (for examples never ending darkness passed a given point).
• Break any law of physics (for example, the trajectory of the sun can be anything, and the gravity does not need to be explain or even explainable without using magic).

It is clear that given all that, the world can not be flat, because if it was, the sun would never disappear behind the horizon. It is possible to give some kind of curvature to the world to avoid this, but then the question of seasons arise.

• Pratchett has slow light in the intense magical field of Discworld, and the sunrise washes over the world rather like a tsunami. Its never explained how eyes function in Discworld. – James K Oct 11 '15 at 19:17
• @Vincent It means that there is no need for that the sun which disappears behind the horizon to be the one which will rise the next morning. A new sun can be created each day, or an infinite number of suns can follow each other, passing through the sky and never coming back. – Kolaru Oct 11 '15 at 21:41
• Why not have the sun disappear into a hole in the ground at night? (This is fantasy after all) – immibis Oct 12 '15 at 0:00
• Are you basically asking about Minecraft here? – Max Williams Oct 12 '15 at 9:55
• @abcde: 'fraction' in the sense of 'part', not the ratio of part to whole. – deltab Oct 13 '15 at 1:13

If you are okay with breaking every laws of physics, simply get rid of euclidean geometry and get "overlapping" space. Your world can be the size and shape of Earth. You start on point 0, walk to East, at some point if you trust stars and such you are back at your starting point, but in fact you got to a second point, overlapping with point 0.

You can make only the Earth overlapping, in this case overlapping areas will share the same stars, the same seasons... Or put some more magic into it and consider that everything share the overlapping geometry. In this case you can just do whatever you want with overlapping geometry as a blanket excuse.

• So, you'd basically change the topology of spacetime? – HDE 226868 Oct 11 '15 at 19:33
• I think it is a really elegant solution. However if you "overlap" your world on the est-west axis, you will get a strange singularity at each pole. Which is... weird. – Kolaru Oct 11 '15 at 19:56
• @HDE226868 yes. and I'm totally cool with that. – Petit Lama Oct 11 '15 at 20:28
• @Kolaru We can still have day/night with a cylinder world. But with a spherical world, the poles could be magical places working like "teleportation" portals. Short-cuts to faraway lands. – Petit Lama Oct 11 '15 at 20:28
• I've seen a story like that. Crossing the pacific went back in time, going around as many times as you dare until the air is not breathable. It was an exercise to make a round shadow but have different geometry. – JDługosz Oct 12 '15 at 7:08

"Infinite" is really a big, big word. If you want to keep any semblance of physics, consider a world that is finite, just really big. Even a mundane Niven ring is big enough for all practical purposes - at 1AU radius, to walk around it would take about 20 thousand years of nonstop walking (and that still leaves several Earth worth of width unexplored). And there are bigger structures possible - an Alderson disk is much, much bigger and if the Sun is made "bobbing" through the hole, you'll have reasonable day/night cycle ,and with some rotation, you'll have seasons. And you can make Niven ring or Alderson disk around Betelgeuse or a quasar for (much) more habitable space.

You can also make the beings smaller - if your humanoids are 1mm tall, even a common Earth like planet will be like an infinite world to them.

And that's still within physics as we know it.

• A quasar is a supermassive black hole emitting lots of radiation. I don't think it would be a good place to live. :-) – HDE 226868 Oct 11 '15 at 23:49
• @HDE226868 Of course you'd place your ring/disk at the appropriate distance. The amount of (hard) X radiation is probably crucial, but I have not been able to find (complete) spectral characteristics of quasars. Relativistic jets are truly dangerous, if they hit the structure, they'll sterilize everything in their path - but they'd do it only with a small fraction of the living space, no more than a square lightyear or so (typical ringworld around a quasar would have the radius of some lightyears). – Radovan Garabík Oct 12 '15 at 12:07
• @HDE226868 Life can adapt to lots of environments. AFAIK oxygen was deadly to the first lifeforms to live on Earth. But life adapted to that. And it has adapted to be able to survive most of the kinds of radiation that we do receive from the sun. – kasperd Oct 12 '15 at 19:08

Well, if you're already accepting that there is some magic, you could try an infinitely long cylinder, orbiting a cylindrical sun.

Obviously in our universe, these would collapse in on themselves lengthwise, but with magic anything is possible.

Another possibility - the world is an infinite sheet, with a hole in it through which the sun passes back and forth. This also gives you a reason for different societies affected by the temperature at different distances from the sun-gap.

• Well, an infinite world can't orbit a finite sun, so the cylindrical idea is the best one so far. +1 – Lucas Oct 13 '15 at 14:28

The world can be made up of an infinite 2-dimensional plane of arbitrary thickness. In this plane, there exists an array of holes which pass through the plane.

For ease of visualisation, the infinite plane would be similar to this picture, but with smaller holes relative to the normal land area than pictured.

Around this plane, there exists an infinite number of suns. These suns periodically cycle between the two faces of the plane, entering a different hole each time.

The suns follow a repeatable pattern in their cycling, and they sometimes spend a shorter duration of time on one half of the plane and a longer duration of time on the other half. Therefore, you get summer on one side of the plane and winter on the other side of the plane. Some suns do not cycle with any variations in their relative time, and these locations do not experience seasons.

This also adds some additional interesting elements into the world, since there has to be, by necessity, regions on this infinite plane that obtain close to zero sunshine (the dark zones). These zones may be inhabited by different creatures.

Also, falling into one of the holes on the infinite plane will allow you to easily travel to the other side of the plane - just make sure not to do it when a sun is setting in your hole!

## Conclusion

The sun travels through the sky and when the night comes it disappear behind the horizon. - Check.

There are places on Earth with seasons. For simplicity, assume it only means longer days with the sun higher in the sky during some periods (summer) and shorter days with the sun lower in the sky during others (winter). - Check.

There are places on Earth without seasons. - Check.

The world looks locally flat (there can be geological stuff, like mountains, but no obvious curvature of the world at short scale). - Check.

The fraction of the world which is habitable is infinite. - This is kind of trivial, since as long as the percentage of habitable surface is nonzero, the total habitable surface would also be infinite.

• Wow! I'm imagining what "from space" sped-up film footage of this world would look like, with all the suns moving in their regular patterns, and it's spectacular! – user867 Oct 15 '15 at 6:28
• Definitely the coolest thing I've ever read on WB.SE – Azor Ahai Sep 29 '17 at 16:39

I had come up with one such world recently.

The habitable surface is essentially along the convex side of a parabola. This can either be just a parabolic ribbon, or preferably along the center of a hyperbolic paraboloid (See the second image at wikipedia, or this image, in which the habitable area is on the upper side of the red arrow), just because I think infinitely tall mountain ranges would be a cool bonus feature.

As you suggested, there are multiple suns (actually infinitely) that pass over the land in a slightly wider parabola. The suns move most slowly at the apex, and move faster and faster at the extremes, so that creatures living on the apex of the parabola experience normal Earth-like days with one Sun which rises and sets, whereas creatures living in the extremes experience "days" that approach an infinitesimally short over-head passage of the sun - with the leading side of the parabola instead having the infinitely many approaching suns placing it in an eternal dawn, and the trailing side of the parabola having the infinitely many receding suns placing it in an eternal dusk.

This would be an excellent discovery - one could start out in an Earth-like world, and as they travel further "West" (toward the setting sun) the days grow shorter and shorter and the dusk longer and longer until at one point they see for the first time a sun rising while one is still setting. Eventually they reach a land of eternal dusk that stretches on forever... an excellent place for vampires and the like.

• The sun travels through the sky and when the night comes it disappear behind the horizon: Not everywhere, but true near the apex.
• There are places on Earth with seasons. For simplicity, assume it only means longer days with the sun higher in the sky during some periods (summer) and shorter days with the sun lower in the sky during others (winter). This can be easily incorporated by varying the path or speed of the suns, nothing more than a hand-wave really
• There are places on Earth without seasons. With complete control over the path of the suns, this is just another handwave
• The world looks locally flat Sure, this just depends on scale
• The fraction of the world which is habitable is infinite. Check
• Could you clarify what parabola you're referring to in this context? For many of us, a parabola is what you get from graphing y = x², and it's not clear how a world can exist on a line drawn on a graph. The "hyperbolic paraboloid" seems to be a saddle-shaped thingy, and it's not clear what the important properties of such a specific shape are that you're leveraging. (I don't see how there's an area of eternal dawn, for instance, but that's just me not having the information available to see how.) – doppelgreener Oct 14 '15 at 12:19
• Yes, that is indeed the kind of parabola I am talking about, however neglected to clarify that the habitable surface would be on the convex side (so, to orient the parabola such that gravity is downward on the graph, that would be y=-x^2 ). And the hyperbolic paraboloid is indeed that saddle shaped thingy, the cross section of which is a parabola – Fabio Beltramini Oct 14 '15 at 18:08
• The "important" property is that the parabola is locally circular at the apex (so it's indistinguishable from Earth) but at the same time, as one travels away from the apex, it becomes increasingly flat/linear. So it's a way of taking an Earth-like place and combining it with a not-at-all-Earth-like place – Fabio Beltramini Oct 14 '15 at 18:17

Now for a truly ambitious setting:

Consider more dimensions. For simplicity, let's assume the planet is a five dimensional hypersphere (there are some good reasons why the number of spatial dimensions has to be odd). The hypersurface is a 4D closed hyperspace. There are 3-dimensional cracks (or just boundaries between geological objects) on the surface, just hairline thick (or maybe planck length wide). Each of these cracks hosts 3-dimensional beings that somehow got into this world, and they are quite unaware of their universe (at least until they start building modern physics theories). The seepage of 5D photons and energy into the 3D subworld could provide some truly fantastic possibilities, there is a lot of 3D subvolume, especially if the cracks are fractal like, and if you somehow manage to cross the extra dimensions, you can get into neighbouring world (which might be just millimetres away in any of the two remaining axis). Yes, this gives extra planes of existence on a scientific basis.

Wizzard's training would include a lot of n-dimensional geometry I guess.

Consider Greg Egan's Diaspora for some mathematical description of 5D universe.

• Why must the number of spatial dimensions be odd? – gerrit Oct 12 '15 at 10:29
• @gerrit In even dimensions, Huygens principle does not work, wave propagation creates "afterglow" long after the wave source stopped emitting. Hearing and vision would be rather difficult. – Radovan Garabík Oct 12 '15 at 11:30
• While it's an interesting factoid that spherical waves don't behave pseudo-one-dimensional if the space hasn't odd dimension, I don't find this a particularly convincing argument that “5D is better than 4D”. Spherical waves still exists in 4D – they just don't disperse linearly, but at length scales much larger than the wavelength this goes largely unnoticed. It's actually quite similar to the behaviour of massive particles: these move according to the Schrödinger equation, which implies quadratic dispersion – but because the wavelength is so small, we usually just observe the Newtonian laws. – leftaroundabout Oct 12 '15 at 19:13
• The standard argument why we need precisely 3 spatial dimensions is that these are required for Kepler orbits. But this question is pretty much about avoiding Kepler orbits, so... – leftaroundabout Oct 12 '15 at 19:16

I'd go with a cylinder world. It would only be infinite on one axis, but you would get the same ground area in the end (infinite).

This cylinder could be orbiting around a cylinder star; if your world's axis tilt slowly back and forward that could give you seasons, but the more you go in one extremity or the other, the more extreme the seasons will be (in both case, your distance to the cylinder star would close to infinity).

Another options would be to have an infinity of small stars orbiting around your cylinder. That would have more possible variations for seasons as you may have them orbiting on an ellipse (a little like comets around our sun), but not be synchronized with each other. Also their distances, sizes, and orbiting speed can vary, which would allow you to have areas with different day length or seasons cycles (you could travel for a few thousands km on a cold/arctic world, then arrive in a tempered or tropical area, etc...).

Gravity and other stuffs should work pretty much like ours so you could have some moons orbiting between the suns, and why not have your inhabitants use artificial satellites.

PS: The cylinder is also rotating along its axis in order to have both seasons and day/light cycles

• I like the idea - an anisotropic universe where gravity does not propagate in the direction of the axis. You'd have even true "vandering stars", small suns that have nonzero axisward velocity component and they just slowly (or quickly) pass over, never to be seen again (they might scorch the landscape, if luminous enough - a nice setting for either an ancient or impeding catastrophe). Thinking more about it, even the main sun can have (very small) axisward velocity and it could drift away over millenia or millions of years, leaving perpetual darkness behind the slowly moving "habitable zone". – Radovan Garabík Oct 12 '15 at 7:44

I've actually wondered about this sort of thing before, this is what I came up with. An infinitely long cylinder with stars orbiting it and moving downwards.

Illustrated path:

\| |
| |
| |
| |
| |\
| |/
| /
|/|
/ |
*| |


If you want to eliminate the "where did they come from" aspect you could say it's a geometric ray rather than line (only expending infinitely in one direction) and at the top of the world there's a super star or star forge type of thing that spits these out.

• I dub thee "Screwworld"! Although I bet doing an internet search for that name might get you some... unrelated... results. Also, if it rotates, apparently it can be used as a time machine. See the Wikipedia article on "Tipler Cylinder". – Doug Warren Oct 13 '15 at 17:19

Physics does not have to be the same. We are already presuming differences in spacetime geometry; why not change some of the concepts as well?

Here, we have things like a constant speed of light. There, why not the appearance of a constant angle to the "sun", regardless of ones position on the plane? It seems as if light rains down from an infinite-distant source, being parallel rays. But there is no source: it's a field of radiation as infinite as the world. An observer with eyes or photographic equipment would image a point at some specific angle, like an infinite-far star, that moves over the course of a day. But there is no star; just incoming radiation that's always in transit.

A hot tiny point is not very cheerful, so other effects blur it out to a friendly 1/2 degree of an arc. This can be done with diffusion zones that lie above the ground and have other effects too, as well as effects of the atmosphere or layers thereof.

It makes sense that the sun would be infinite too, right?

• Similar odd lensing effects for sunrise and sundown? – doppelgreener Oct 14 '15 at 12:30

For an annoyingly trivial answer, simply make the planet an infinite sphere, and make the sun infinitely big and infinitely far away.

That is, imagine a spherical planet that goes around its sun much like our Earth does, but imagine the people living on its surface are infinitesimally small. Then for them the surface they are on is infinite, but up in the sky they can see the sun (and, if you wish, moon, stars, other planets etc.) behaving in just the same way that we see on Earth.

This world is quite different from ours, not just in terms of physics but also in terms of mathematics. There are mathematical systems in which the concept of "infinitesimal" makes sense, such as the hyperreal numbers and the surreal numbers, but it is not currently thought that these are relevant to the physics in our universe. (At least, not as far as I know.) But for a fantasy world I think it could make sense.

If you don't like nonstandard analysis, you can approach this in a more "classical" way by taking the limit of larger and larger planets. That is, suppose you can create a planet and star as big as you like, while adjusting the laws of physics so that normal-sized people can still live on its surface. (Gravity will have to become weaker, obviously, and the speed of light will have to become faster if you don't want the planet's orbit to be relativistic.) Then imagine a sequence of larger and larger planets, and by taking the limit of this sequence you can consider a planet of infinite size.

Of course, you don't have to go all the way to infinity if you don't want to - a planet of galaxy size, or the size of the known universe, would be just as good for all practical purposes, and in some ways is more interesting to imagine.

• +1 I find this to be a very important trivial answer. If this is not "the natural solution," then that suggests that the concept of an infinite world is not quite what the OP intended, and forces them to dig into what they really want. (However, one caveat: if its infinitely far away, with a finite angular velocity, its has an infinite velocity... this causes issues if the rules of relativity are in effect in this universe) – Cort Ammon Oct 12 '15 at 22:25
• @CortAmmon that's true. I actually had a sentence in there originally about how these people can never reach the moon because it's infinitely far away, but I quickly edited it out when I realised light can do it in finite time in this universe. Light must be infinitely fast on the scale of people, but it can still be finite on the scale of planets. – Nathaniel Oct 12 '15 at 22:47
• If the radius of the sphere is infinite, I do not quite understand how it could have a surface. In the other hand, I think that the infinitesimally small folk trick can work (since hyperreal numbers share much of their properties with reals). However, since any finite real distance looks infinite for a infinitesimally small guy (he needs an infinite amount of steps to travel that distance), that means that all the surface he can reach in finite time will have the exact same sun cycle. Strictly speaking it still answers the question, but it is worth mentioning. – Kolaru Oct 13 '15 at 18:50
• @Kolaru suppose the infinitesimal people measure part of their body and call that distance a cubit. Then the radius of the planet is an infinite number of cubits. (Since this world is based on a nonstandard number system, an "infinite number" really is a thing here.) So having infinitesimal people on a finite world is the same as having finite people on an infinite world. – Nathaniel Oct 13 '15 at 23:26
• You're right that the sun cycle doesn't change within "normal" travel distance, but note that some things do travel infinitely fast here (such as light and planets), so you could make it possible for people to travel that far if you wanted. – Nathaniel Oct 13 '15 at 23:27

As Radovan Garabik said, you don't really need infinite so long as it's bigger than you can travel in a lifetime. So long as you are limited to low tech transport that means structures at star-system scales are big enough.

Now, for something that comes close to what you're after and doesn't break any laws of physics (but would require some incredible engineering!)

Niven's ring as designed is impossible because it requires materials beyond what chemical bonds can possibly do. However, this doesn't rule out all rings.

Step #1: Gather a bunch of stars. These orbit in a rosette, the larger the better but you need a lot of stars.

Step #2: Build something akin to Niven's ring but instead of the retaining walls the sides simply gradually climb to the requisite altitude. Note that this ring's distance from the rosette is a bit greater than Earth's distance from the sun, the overall ring is much bigger.

Step #3: Just outside this build a far more massive ring. The junction between these two rings is a magnetic levitation system. Think of the habitable ring as a truly enormous maglev train except it's a complete ring so there's no start and end.

Step #4: Spin the habitation ring, de-spin the ring behind it. You can get 1g on the inside of the habitation ring without super-strong materials this way as the average velocity of ring + backing ring is orbital velocity for it's distance from the center of mass of the system.

Results: You have a land that's perhaps a million miles by a billion miles. The inhabitants don't even realize there are edges as the slope is gradual--to them it's simply terrain that gets too high to cross.

You have stars that cross the sky from pretty close to the horizon to pretty close to the horizon. (The bigger the ring the closer to the horizon they'll get.) You can even have seasons by having stars of slightly different brightness. I haven't tried to solve this for possible values, I don't know if you can match Earth's day and year. (And if you can note that it means 365 stars in the rosette!)

Beware that the ring is unstable and the rosette is unstable. Without some stationkeeping system the whole thing will end in catastrophe in time.

Some possible tweaks:

You could have a black dwarf in place of a star. The result would be a day that doesn't happen.

If the atmosphere is thick enough (creatures evolved for it won't care, flight will require less wing span) you could even have a neutron star in place of a star. No day but the effects of one of it's jets touching the atmosphere would be an incredible aurora. Note that the jets remain at a fixed orientation in space as it orbits and thus will hit in different locations on different passes.

You can't have moons but you do see the more distant stars in the rosette, it will never be truly dark. (The nearby ones that have dropped off the horizon are cutting through so much atmosphere that they won't be seen.)

Remember that under general relativity, gravity affects light. Imagine an infinite wall that divides the universe to two halves. Details can vary, but for example if it consisted mostly of stone and was 10 000 km thick, the gravitation would be around the 10 m/s2 seen on Earth.

Now, a sun moving above the plane at constant height will eventually disappear behind the horizon, not due to curvature but due to gravitational lens effect. Thus, the world needs an infinite stream of suns, spaced at suitable intervals and moving at suitable speed to provide a day cycle. The path taken by the suns can vary between times of the year to provide seasons.

Some of the implications of such world are:

• Orbiting satellites are not possible.
• There will be regions where no sunlight ever lands (too far to the sides from the path of the sun).
• Digging down 10 000 kilometers will bring you into a brand new side of the universe :)
• Like @Kolaru mentioned in a comment, due to same gravitational lensing, one would see parts of further-away land above the horizon. Atmospheric refraction will limit the distance, but it would probably seem a bit like as if you were in a deep valley.
• In my understanding (which is very partial) the gravitational lens effect will not make the sun disappear, but rather bend the light such that you will be able to see the whole infinite wall (i.e. the light emitted by the wall at low angle will not be able to escape into space, but will eventually fall down on the wall). – Kolaru Oct 12 '15 at 11:43
• @Kolaru In my understanding, gravity acts on light similar like it does on ordinary objects. Just that light's speed is faster and weight is quite small. But nevertheless, light leaving the sun at any angle, would "fall down" and hit the plane at some distance. When the sun is farther than that distance, it will disappear. – jpa Oct 12 '15 at 12:53
• I did a bunch of math, and the result for a star within 1 AU of the wallplanet is a maximum distance of about 0.95 light years if we treat light as a ballistic particle in a 10 $m\over s^2$ acceleration field. Light will go vertically about 0.48 ly if you can fly that high. Of course, most of the light will be concentrated under the star in a relatively narrow area. – MichaelS Oct 13 '15 at 4:19

One idea is to have your world be a $3$-dimensional subset of a $4$-dimensional space. And your sun (or suns) are regular stars moving along the fourth spacial dimension. We can only see them when they cross our special $3$-dimensional space, and they are invisible otherwise.

Since this is a bit complicated to describe, let us reduce this by one dimension, and imagine we want to build a $2$-dimensional world, that is a sheet-world. In this $2$-dimensional setting, planets and stars look like discs. We live on the surface of a disc which is big enough that is seems "almost" flat. What would an infinite world look like? Well basically you have one horizontal line that splits the world into two regions: above the line is the air, and below is the ground. Now what are the suns? Well they are balls (regular, 3-dimensional ones)! We usually cannot see them, but sometimes one crosses the sheet of paper that makes our world, and then we can see it. At first the intersection of the ball with the plane is a very small disc, which makes a nice sunrise (or 'sunswell'?). Then it becomes bigger until most of the ball has crossed the plane, and finally you get a sunset ('sunshrink'?).

How and why there are seasons depends on how and why do the suns move, so it is entirely up to you. Maybe the suns stay on the same track and every morning you see the same sun? But there could also be a stream of suns that all follow the same path and every morning you see a new sun. Finally the movements of the suns could be very chaotic, so that some areas stay in the dark for ages before being once again habitable by human beings.

If you want to get creative, you could also say that sometimes, suns do not cross our dimension above the ground, but below, melting the rocks around them: that is how volcanoes are made...

You could also say that there are many other sheet-worlds: usually they are far away and we cannot see them, but sometimes two sheets come really close and strange things happen, like people and objects appearing or disappearing randomly (or on purpose) by switching sheets.

• No need for multiple suns if there's one that's infinitely bright and infinitely far away. (+1 by the way) – MackTuesday Oct 12 '15 at 15:49

If I was to make an infinite world in an imaginary realm there would be no singular sun. Imagine a blanket of star, similar to our own sky, but with more color variation. Now imagine these "stars" grow and fade in brightness (each in their own rhythm). Some might brighten to the point of a typical sunny day but fade back within minutes. They could flare to brilliance almost instantly or slowly like a dawn. They could fade to pricks of light of vanish completely. They could be different sizes, colors, intensities and positions. Of course there is nothing to say only one would grow bright at a given time. You might have 2, 3 or even a dozen producing light at a given time.

As long as the system is backed by predictable math it will close enough to reality that person can understand and follow it, but at the same time it's completely alien. The player might not understand the system perfectly, but your NPCs would usually understand the common and typical behaviors of their stars.

This leads to incredibly rich possibilities of events and world effects that go far beyond predictable and highly repetitive day and night cycle.

Omens and portents of the pale golden star. Wild celebrations when stars all go dark with bonfires and lights everywhere. Times a year the yellow and the blue stars flair bright for several cycles and the sky is filled with a green light which makes all the plants grow at an insane pace (farmers everywhere could plan crops for these time). Think of a time when a half dozen stars all become super bright and the world is a bathed in blinding light and heat. You could need special protective/reflective gear and have most places would be closed up tight. It would be a rich alternative to the typical "night bad."

So short answer... any shape you want, even a simple plane. It wouldn't matter because your light is fixed points.

• Hi DBD and warm welcome to Worldbuilding. Could you clarify your question, as I'm not sure what you're asking. Are you asking about the mechanics, or the problems with the scenario, or...? – Mikey Oct 12 '15 at 18:27
• @Mikey - I'm not asking a question. This was posted as an answer. – DBD Oct 12 '15 at 18:38
• baha, sorry, I was reading this in a "first posts" review and thought it was a question. – Mikey Oct 12 '15 at 18:50

So, let's start with a completely flat planar world. This doesn't quite have a "horizon" in the normal sense, as from a suitably high point you can see forever. You can only have a horizon on an infinite world with a cylindrical, parabolic or conic(!) world.

Then imagine a single sun tracking across the plane forever on an infinite line. Each place beneath it experiences a single day. Everywhere else gets arbitrarily dim twilight: the sun gets smaller and dimmer as it departs, until it's as dim as the farthest star on the edge of our universe is to us, and then dimmer still, but it never sets.

Now consider a line of these suns passing over "east" to "west", at 24h intervals. The trajectories are not entirely the same: each appears slightly "north" of the other, with another sun's track gradually approaching from the "south".

In summer, you have suns passing overhead. In winter, you see two suns, but they are both too distant to warm you well. At midnight in midwinter, there are two suns rising and two suns setting, all in the far distance.

(Gravitational trajectory of photons or indeed the suns themselves not considered. If you want the sky to be dark the photons have to escape off into space, otherwise a telescope pointed at any angle other than straight up will be able to see ballistic photons from some other part of the infinite surface. It may be easier to have a moving 'firmament' at a fixed altitude which the stars are stuck to or holes in, and which also absorbs stray photons.)

This is perhaps a similar premise to Amber. The centre of the universe is the pattern in Amber. Amber is the area around the pattern, and it casts Shadows - sort of onion layers around Amber, such that the 'closer' you are, the more similar things are.

Those who walk the pattern are able to navigate through Shadow, by changing one element at a time as they walk. If they walk far enough, they can reach anywhere or anything - but the stranger the 'rules' are, the further you are away from that anchor of reality in Amber.

In this way, the central city - Amber - follows a pretty conventional pattern of life. It's medieval ish, and is particularly stable - fires burn, but gunpowder doesn't explode. This means that it's effectively limited to 'sword and sorcery' but at the same time allowing things like our world of Earth (with guns and nukes) to exist. You just have to travel out a distance into Shadow to make it happen.

So by being so - there are an infinite number of shadows. As such, an infinite number are habitable, and likewise an infinite number are similar to the sun cycle of the prime.(amber).

The futher away you shadow walk, the wierder stuff gets. The premise of amber hinges on a limited number able to travel between shadows - shadow walking being easy ish, but only conferred by the Pattern. Other lesser talents like science, magic and a diverse range between may have a limited degree of ability to shadow travel.

• what does that have to do with infinite living space and sunrises? – JDługosz Oct 12 '15 at 11:32
• Parallel worlds present infinite living space. In an infinite configuration of parallel worlds, an infinite number have similar sun cycles to the prime. – Sobrique Oct 12 '15 at 11:35
• You should add that to the Answer! The topic sentence "this is similar to Amber" makes no sense without the explaination, since we are initially thinking about an infinite plane. The details of tech. Is not relevant: instead explainnyour idea that an infinite number of ordinary balls will do given suitable connectivity. – JDługosz Oct 12 '15 at 11:53

No need for a sun to travel in a straight line; each sun simply travels along a gigantic circle at some fixed (gigantic) altitude.

You could then get a variety of effects by having suns move at different speeds, different length orbits, the orbits drift or wobble around, the altitude varies.

An interesting, novel variation on seasons is a region that sees two suns of slightly different orbital periods.

During the the mild season, the suns are completely out of sync; each "day" has two periods of light and dark and mild temperatures, and weak winds.

During the intermediate seasons, the suns are only partially out of sync; the second sun comes along in the wake of the first, leading to each "day" consisting of one long day period and one long night period.

During the stormy season, the suns are completely in sync; each "day" consists of a short, intensely hot period while both suns are blazing, a short, extremely dark period, and long twilight hours that suffer strong storms as the hot, moist air beneath the suns blows into the colder regions.

Tolkien did fine without a sun in his land.

How about a line rather than a point as a light source? If the world is finite east-west but infinite north-south, the line also runs north-south.

• Yes, that's basically Roland Heath's cylindrical world. Would make truly impressive dawns:-) – Radovan Garabík Oct 12 '15 at 8:18
• Tolkien did however use a sun, both the Hobbit and LotR are set in the Third Age of the Sun – Jimmery Oct 13 '15 at 14:57
• @Jimmery: that was a flagrant gimmick to boost ratings following the sunless "Lamps" and "Trees" seasons. Fans vary in their opinion as to whether Tolkien "did fine without a sun" in that work or not ;-) – Steve Jessop Oct 14 '15 at 1:09

How about an infinite number of Earths orbiting an infinite number of stars?

If the ability to walk infinitely on your own two feet is critical, then introduce artificial mechanisms which manipulate physics to keep some or all of the planets very close together (a mile or less, perhaps). Then you simply walk to the point where two planets are closest together, and then jump and float to the next planet (gravity at this point would be near-zero).

Something which maintains an appropriate atmosphere across this "gravity bridge" would probably be necessary, or else some kind of space suit for the low pressure and oxygen.

The "stars" would have to be appropriately scaled to fit in among the planets without scorching them.

## Menger Sponge Earth

An idea to provide for an infinite habitable space would be to use a Menger Sponge-like Earth, where the Menger Sponge is a 3d-fractal, with a infinite surface area, contained in a cube-like shape therefore resembling:

To simulate the cycle of season you could make the Sponge rotate around a source of light (similar to a star) situated in the middle. Of course this will create some areas always in the dark, and others always illuminated, however this is permitted by the question. A solution to this problem could be to add a fractal system of stars, with a new sun placed at the centre of the cube holes in the sponge

• A lightsource in the middle would make for no day/night cycles at all. Maybe better have it outside? – Paŭlo Ebermann Oct 12 '15 at 21:41
• @PaŭloEbermann would it? I think that if we apply rotation to the Sponge it could work, with some holes being in the shadow for certain periods of the revolution and some in light in the same period. There would be of course areas where no change is present, but that was permitted by the rules. I think nonetheless that putting the light outside will work as well, with the same drawbacks as well (areas perennially shaded/lit) – WizardOfMenlo Oct 12 '15 at 21:45
• I assumed a circular/symmetric lightsource – if that is in the center of your sponge, the sponge can rotate as it wants without changing anything. If the lightsource moves around in the center, or is not symmetric, it might change something. – Paŭlo Ebermann Oct 12 '15 at 21:49
• Not sure this satisfies "infinite habitable surface". Of course it has infinite surface, but only finitely much of that has sufficient headroom to be habitable. – Steve Jessop Oct 13 '15 at 2:45
• @SteveJessop you're right, the surface for all practical purpose isn't, strictly speaking, infinite. It is for sure really, really big. To render it habitable to all levels we could recur to some magic and make habitants smaller on different level, having therefore a "fractal population" :) – WizardOfMenlo Oct 13 '15 at 6:04

Infinity is really something that we can't discuss while not ignoring the laws of physics altogether. But what if your world is not completely infinite, but just incomprehensibly huge? Imagine a gigantic Dyson sphere. I mean a really big one with a radius of 100 million kilometers which has been built by an ancient, but now forgotten civilization. This Dyson sphere is peculiar in that it has inhabitable lands and an atmosphere on the outside. They have built it around one star in a binary star system where the other star is quite a large distance away, but shines very strongly. As the sphere rotates and the stars orbit each other, the surface of the sphere experiences normal day/night cycles, and its surface is 400 million times as large as the earths, which for all intents and purposes of a civilization on the ground can be considered infinite.

Perhaps you're thinking too much of the universe your characters exist in as a standard universe.

Imagine two gravitational forces, one that pulls matter together, then another that pushes everything away.

This universe would be an enclosed sphere around a singularity of light. This light pushes everything equidistant from itself. Think of Earth, with a sun in the center of it, then the people would exist inside, being pushed downwards to the ground by the light singularity.

Two things can occur now;

1. As time progresses, the sphere grows. This quite literally creates endless space to discover.

2. The sphere does not grow. Instead, if your races dig deeper, they find more spheres surrounding the one they are enclosed in, much like digging underground and finding a huge cave... except that the light permeates the ground as well. I'm sure someone can come up with a radiative light source that, to the human eyes, looks like regular light, but can pass through regular solid matter.

I prefer the second solution because entirely new worlds can be discovered. What's normal on one 'plane' of existance may not be on another.

Charles Stross in Missile Gap explored the consequences of remapping Earth on a (practically) endless flat surface called an Alderson Disk. ICBMs do not work any more, deterrence changes completely...

You don't NEED truly infinite space (just enough that there is no possible way to travel any appreciable fraction of the distances involved within the life of any individual in the universe you create) but you can have it; there's a lot of world-like structures in Science Fiction that you can take inspiration from 3D fractal structure "worlds" are one but I'd favour Cosmic Macaroni in the name of simplicity. This world is an infinitely long tube that spins around it's long axis to create outward pseudo-gravitational acceleration, the tube is arranged in a very loose spiral, the curvature is invisible from the ground, as is the upward curvature of the ground, due to the scale of the object, but it still creates a vanishing point for the "sun" the horizon is reversed for some observers but it's still there. Sunlight, seasons, weather, etc... are all created magically, using a series of artificial suns (of variable temperatures) that pass down the long axis of the tube (at variable speeds), varying (or not varying) the relative temperature and speed of successive suns passing over a given area creates seasonality or non-seasonality. The local weather cycle works just like on Earth but over much larger surface areas so winds will tend to be stronger and more sustained. The glare of the suns washes out any view of the overarching terrain during the day moisture haze blocks light from fires etc... that would otherwise be visible at night. The other major, and it is really major, piece of magic is in preventing the whole thing collapsing into a sphere under it's own mass. There are several disadvantages to this set up; you can't really do any mining here, there's no material to mine into, you'd just cut out into space which would have catastrophic results for the whole system. You can also eventually walk around a given loop of space within the tube so it's only infinitely large in one direction so to speak, although I think you could configure the terrain (in particular the oceans and mountains) to create the illusion that this was not the case by preventing anyone actually accomplishing a circular circumnavigation instead pushing them into a spiral of travel. Last but not least it is possible that an observer at a sufficient altitude might be able to spot the structure of things if the air at altitude was very dry for some reason.

I'd like to point out that this structure could also be build on a smaller scale with less regard for a normal, read Earthlike, appearance without using any magic at all. Pat Gunkel designed it, at the near infinite scale it's called aegagropilous galactotopolis and it looking like a galaxy wrapped in angel-hair pasta.

Infinite sphere.

The simplest answer to replicating all Earth conditions is to replicate Earth's geometry.

Either the planet will have to rotate on its axis infinitely fast, or if it's a geocentric universe, the sun will orbit infinitely fast. The sun's energy output must likewise be infinite.

One consequence of this (and many other geometries) is that each latitude belt is itself infinitely wide. Thus, it won't be possible to travel to other climates.

## protected by James♦Oct 12 '15 at 18:48

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