If it is possible for a computer in the first dimension to perform a second dimensional operation in the same way a computer in the second dimension can perform a third dimensional operation, then maybe a third dimensional computer could perform a fourth dimensional operation.

We already have 2d computers, so what i am wondering is how would a 1d computer work out multiplication. I've theorized that the physics of this 1d world that it is built in would have 8 characteristics to work with:

  1. length is mass
  2. there can be charged particles(lines) that attract/repel each other
  3. there can be gravity of attraction or repulsion between masses(your choice)
  4. there can be lines splitting or combining, but the rules for both must be given.
  5. there may be limits set on the world (example: a speed limit like the speed of light. or an edge where things )
  6. there can be "optimal lengths" where a line is more/less stable(optional)
  7. we are only allowed to put "input lines" (which will be multiplied) into either 1 area or two
  8. the outputs may be anywhere, but you must be able to read them all.

what determines a successful "computer" would be if it is capable of multiplying any single digit number from 0-9 with another from 0-9.

edit: if it makes it easier to think of, the whole system can be reset each time you want to use it with new inputs(i realize it would be nearly impossible to reset itself).

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    $\begingroup$ I think we already have this, right? All of the data on a spinning disk hard drive is stored basically in a string of numbers, which is etched into a spiral shape. So in effect, all of our math operations are already 1D. If I’m understanding the requirement correctly. $\endgroup$ – Vladimir Nov 22 '18 at 6:18
  • $\begingroup$ Welcome to worldbuilding. Please visit the help center and take the tour to understand what kind of questions we answer here, and then please try to clarify your question. I have problems understanding what you are asking. $\endgroup$ – L.Dutch - Reinstate Monica Nov 22 '18 at 6:20
  • $\begingroup$ @Vladimir you could theoretically unfold a disk that way and you would have the memory, but how would it perform any operations? $\endgroup$ – Blue Piston Nov 22 '18 at 6:32
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    $\begingroup$ I'm not sure I follow your meaning when you say "second-dimensional-", "third-dimensional-", "fourth-dimensional operation". Performing math in multiple dimensions is really just performing math in the one dimension, multiple times in series. $\endgroup$ – Cadence Nov 22 '18 at 6:56
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    $\begingroup$ @CortAmmon, While what you're saying has a geek factor that is, frankly, off the charts, I simply can't tell if by saying "one-dimensional" the OP means the programmatic context of Rule 110, or spacially 1-D (e.g., a line if considered from the point of view of a cube as 3-D, or a single point if we're counting vertices). The reason I point this out is because the question, as written, doesn't suggest the sophistication to understand Rule 110, and therefore suggests that "one-dimensional" is referring to spatial dimensions. It'd be nice if I was wrong, of course. $\endgroup$ – JBH Nov 23 '18 at 0:02

You may wish to look into Turing Machines, a mathematical model that is a one dimensional string of on/off states and a ‘moving head’ that can move up and down the line and alter the state of the bits. Any computer algorithm is theoretically possible on a correctly made Turing machine. A full 6 step algorithm for simple multiplication can be found here (I’ll transcribe the steps to this answer when I can).

If your universe is capable of sustaining anything that would care about this computation then it must also be capable of sustaining such a construct. Voila: 1D computers.

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  • $\begingroup$ A virtual implementation of a Turing machine can be found in the programming language Brainfuck (en.wikipedia.org/wiki/Brainfuck), the recipe for multiplying two numbers is on the wikipedia page. Several real world interpreters for the language exist and there are tags on other stackexchanges (codegolf, softwareengineering, codereview and stackexchange itself). $\endgroup$ – GretchenV Nov 22 '18 at 10:19
  • $\begingroup$ @GretchenV My personal favourite brainfuck variant is Ook. $\endgroup$ – Joe Bloggs Nov 22 '18 at 12:11
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    $\begingroup$ Not really 1D, even a Turing computer needs two dimensions, one spatial and on temporal. $\endgroup$ – Kain0_0 Nov 23 '18 at 0:29
  • $\begingroup$ @Kain: if you discount time as a concept the the OP’s characteristics 2,3,4 and 5, along with the concept of ‘output’ are all impossibilities. Add to that the fact that we’re currently unsure how many dimensions we live in and I think it’s pretty clear the OP was referring to spatial dimensions. $\endgroup$ – Joe Bloggs Nov 23 '18 at 7:07

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