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Assuming that we have a universe with four spatial dimensions plus time, within which atoms exist that can form solids, liquids, gases and plasmas, the compounds that can be formed having physical properties equivalent to those in our 3D universe, such as mass, friction, elasticity, hardness, strength and suchlike.

Within this universe, within a portion of it with solid, liquid and gaseous matter that has a 'down' direction with solid matter below, there exists terrestrial 4D sentient beings who have conceived a desire to modify their environment and to build tools and machines to make their lives easier.

What physical tools and machines are possible in 4D space?

In particular:

Are there any machines that exist in 3D that are not possible in 4D, and are there any machines possible in 4D with functionality that cannot be duplicated or approximated in 3D? Examples addressing equivalents (or lack thereof) to common 3D machines would be appreciated.

Are there any online or offline resources that discuss and provide examples of mechanical systems in 4 spatial dimensions beyond the properties of simple 4D shapes?

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  • $\begingroup$ Are you sure you wouldn't prefer 5 dimensions over 4? Odd numbers are better. (Maybe it doesn't matter so much for mechanics, but you might want something like electric motors...) $\endgroup$
    – JDługosz
    May 10, 2016 at 8:56
  • $\begingroup$ Asking multiple questions in one is not recommended as it makes it hard to answer with a concise and focused reply. Additionally it becomes much harder to rate answers as to whether one is better than another as the "best" answer to each part of your question may be held in different answers. See tips on how to fix the problem. $\endgroup$
    – Tim B
    May 11, 2016 at 12:29
  • $\begingroup$ @TimB, Thanks. I suspected that I was getting a bit wordy. How's my edit? $\endgroup$
    – Monty Wild ♦
    May 11, 2016 at 23:00
  • $\begingroup$ Yeah, looks much better :) $\endgroup$
    – Tim B
    May 12, 2016 at 8:16

2 Answers 2

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For one thing, spiral galaxies and planar solar systems would not exist because the principle by which the sum of all particle vectors average into a flat plane only works in 3 dimensional space (according to mathematicians) Intensities would depreciate over distance at a greater rate. Mass would be more concentrated as atoms pull together in 4 dimensions. Physics would be fundamentally different. Generally, this universe would be way more different than you probably realize or can even conceive.

Any 3D machine would work, provided that you supply a physical barrier to constrain it to 3 dimensions.

Computers would be immensely more powerful and compact because the transistors can be packed into more dimensions while still having air flow and having an unobstructed path to the motherboard. (currently we are approaching the limit of how powerful a PC can be whilst using 2 dimensional IC layouts)

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    $\begingroup$ If you follow the first link, you'll notice that the universe I talk about is largely solid, and has no galaxies or solar systems - it is intended to be (at least conceptually) procedurally generated. In this universe, mass is not attracted to mass, it is repelled by vacuum. Are you sure that an electric motor would work? I'm not sure if electromagnetism is possible in 4D. $\endgroup$
    – Monty Wild ♦
    May 10, 2016 at 5:09
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    $\begingroup$ I'm not sure either. But if we are inventing rules like "matter is repelled by vacuum", then we may as well also invent rules like "electromagnetism works in the following way...." $\endgroup$
    – Lorry Laurence mcLarry
    May 10, 2016 at 5:15
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Reduction drives could be more flexible in 4 spatial dimensions than in our 3D. Also, parts rotating about two orthogonal planes independently certainly would have applications in mechanics.

Discussion about fields (analogous to the EM field in our space-time) requires more specificity about “4 spatial dimensions + time” setting – is it pseudo-Euclidean along the lines of familiar Relativity, or ?

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