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This creature exists in an infinite world, a flat landscape that extends ad infinitum, where light rains from the sky from infinity during recurrent day-night cycles, and, similarly, the ground goes down continuously.

All kinds of critters populate the cosmos including the skies and the underground realm. This bizarre world has existed for an infinite time and for this reason I want (at least) one creature to have inhabited it for an infinite time. And that's not all, this particular being is also physically infinite(its body has no end); obviously I don't want it to take up all the space, but only a part of it.

In the specific I was thinking of giving it a shape similar to something like Gabriel's Horn, so it would leave a large area available, however this would basically cut most of the surface in half, and on top of that most of his body is vulnerable to attack since it's so thin; for this reason I would like to avoid "infinitely small" bodies.

What infinite shape can I give my organism so that it wouldn't be too vulnerable but at the same time leave room for people to move about relatively easily, without cutting off parts of the world that are close by from each other? Also, while its body is infinite it should have only one head.

I am going to be a bit lax with the physics of this world to allow for some basic functionalities, but I want to put special attention to this aspect.

EDIT: Thanks a lot to everyone for the inputs, I went with the answer that better fits the requirements, but I will probably incorporate elements from other interesting answers

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    $\begingroup$ A creature that is physically infinite in an infinite universe...but isn't actually infinite? I love it! $\endgroup$ – EveryBitHelps Apr 24 '18 at 14:55
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    $\begingroup$ Reminder to close-voters: The problem cannot be fixed if the OP is not made aware of it. $\endgroup$ – Frostfyre Apr 24 '18 at 17:17
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    $\begingroup$ That being said, I fail to see how one answer can be judged as "better," "more complete," or "more applicable" than another. A creature with long legs is just as viable as a creature that floats, for example. So either I fail to understand the question in its entirety, or it's primarily opinion-based. $\endgroup$ – Frostfyre Apr 24 '18 at 17:20
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    $\begingroup$ While I see @Frostfyre's point, I disagree that this question deserved to be closed. The OP provided criteria (not too vulnerable, room for others, can't cut off parts of the world, one head) and the answers generally reflect this criteria rather than being all over the map. If an OP provides all the criteria to guarantee only one right answer, then 99% of the time the OP has the answer already. I'm voting to reopen. $\endgroup$ – JBH Apr 24 '18 at 17:37
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    $\begingroup$ @JBH I've opened a meta thread on this question. $\endgroup$ – Frostfyre Apr 24 '18 at 21:12

37 Answers 37

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The first thing I thought of is that the creature is the ground. Assuming that the sky is infinitely high and the ground infinitely low and the x and y dimensions are also infinite, then the ground occupies half of the universe.

By the definition of infinity, half of the universe is still infinite.

The head could be somewhere in a cavern where beings go through the dangerous way to consult the infinite being's wisdom.

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A snake that is never completely on the surface.

Instead, the snake's infinite tail is always buried inside the infinite ground (e.g., perpendicular to the ground's surface).

Thus, the snake's "base" position is fixed throughout its lifetime, just like a tree, but this snake has the ability to extend in and out as it wishes to.

When it needs to hunt, it can extend out of its hole for kilometers, then it retreats back. Optionally, the snake could be completely buried during the night.

At all times however, its infinite tail is buried infinitely deep.

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Your creature can look however wide or tall you want it to look, but only if the infinite dimension is in one direction like a snake, centipede, etc. If the creature moves exactly at the speed of light, you can use the special relativity length contraction equation: equation

The apparent length to any observer will be arbitrary, could be long, could be short, probably finite because your calculated length is 0 * ∞ which is a meaningless number. People can only observe it in 2 ways: some sort of instantaneous snapshot which will show that the creature is finite, or the observer could catch up to its speed and see it extending into infinity.

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Since no one came up with that: give your creature a simple torus shape, like a donut. This body has no end, as required.

You can select out specific positions for having a head or tail that extends from that torus, but basically it will have no "end".

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Here's the problem: an infinite thing, by default, goes to infinity. And most infinite figures go to infinity on both ends. For any given shape that folds in on itself infinitely on one side, there's no reason it shouldn't extend infinitely on the other. Gabriel's horn is infinitely wide at its "mouth," because it never reaches the x=0 asymptote, just as it is infinitely long at its "tail" because it never reaches y=0 - and you get infinite size. A Sierpinski pyramid can subdivide itself infinitely, but there's no reason that any given pyramid wouldn't be a subdivision of a larger one - extending infinitely. This holds true for most other figures too.

The only figure I can think of that wouldn't violate that principle would be the Koch curve - it's demonstrably of finite area, but of infinite perimeter. However, it's two-dimensional, and also the pieces of the outside are infinitely small, which you said you don't want. Outside of that, I don't know.

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Gabriel's Horn

That's a good shape for your infinite creature because it means it got an finite (and even a small one) volume and mass. But also note the tail diameter decreases asymptotically nearing zero. It means at a arbitrary lenght the diameter becomes smaller than an atom radius, geez it little more and it will become smaller than an String. That being said you don't needs to worry because after an arbitrary lenght set by you the "tail" cannot be visible and after a while it cannot be hit, cut or even interact in any (know) way (not even by a laser).

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I would go for a sphere, made of mirrors that absorb the light and everything that comes to it, no face or anything just a living object with infinite interior, doesn't matter the exterior dimensions. "A living blackhole".

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    $\begingroup$ Welcome to worldbuilding.SE! When you get a moment, please take our tour and visit our help center to learn more about us. This is a clever idea, but to be a suitable answer it could use more description of how such a creature would exist. I get what you're saying about the infinite lighting effect with multiple mirrors, but how would such a creature exist? Thanks! $\endgroup$ – JBH Apr 25 '18 at 21:11

protected by James May 1 '18 at 17:57

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