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1. Life can exist in 3D. 2. A 2D or 1D computer can simulate life in 3D. 3. Therefore, life can exist in 2D or 1D.

a_wild_dandan 7y ago
> A 2D or 1D computer can simulate life in 3D. Can it? I'm not familiar with the limitations of lower dimensional computation, but it sounds like a fascinating subject.
- Will_Parker 7y ago
  https://en.wikipedia.org/wiki/Rule_110 https://en.wikipedia.org/wiki/Rule_110 A Turing Complete 1-dimensional cellular automaton. Also Conway's Game of Life is a rabbit hole you could literally spend your whole life studying.
  - empath75 7y ago
    That is life like but I would not call it life.
    - jolmg 7y ago
      That's the issue with this question. What is life? Common definitions would never think to consider anything other than things in our 3D physical world. Can Life Exist in 2 and 1 Dimensions? Sure, if we're willing to define "life" generically enough. If not, then no.
    - iso-8859-1 7y ago
      Since the universe may be encoded on lower-dimensional boundary, that means that you are not alive, per your definition: https://en.wikipedia.org/wiki/Holographic_principle https://en.wikipedia.org/wiki/Holographic_principle
- jolmg 7y ago
  I believe weregiraffe is referring to this[1][2]. Conway's Game of Life is a 2D "world" with 4 rules that define the "physics" in that world, and someone made a Turing Machine in it. [1] https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-Machine-Life.pdf https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-M... [2] http://www.rendell-attic.org/gol/tm.htm http://www.rendell-attic.org/gol/tm.htm
- Koshkin 7y ago
  One can simulate life using Turing machine.
IanSanders 7y ago
I'd say approximate, not simulate. Or simulate an approximation of 3D. (You need infinite 2D space for a complete model of a finite 3D space)
- ralusek 7y ago
  Why do you need infinite space? The number line of real numbers is basically a 1d space, and we can simulate finite N dimensional spaces with finite real numbers.
  - IanSanders 7y ago
    Let's say you want to represent 1cm*1cm 2d space in 1d. There is infinite number of points in both dimensions of this space. While you can completely represent one of its "slices" with a 1cm segment of 1d space, for a complete model you will need infinite number of 1cm segments stacked, thus requiring infinite 1d space.
jackweirdy 7y ago
Is a simulation of life the same as life?
- sysbin 7y ago
  Yes. People don't have any real control with what happens in their life. Similar to a computer simulation with 3d objects.
  - NickM 7y ago
    People don't have any real control with what happens in their life. Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something. Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Is subjective experience simply a side effect of certain types of computation? That may be true, but if you believe that, you start to get into some profoundly bizarre implications about the nature of reality. Check out the novel "Permutation City" by Greg Egan for a great exploration of this topic.
    - sysbin 7y ago
      > Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something. I disagree with your interpretation of control. The word is human expression and shared between one another. So you can have a different understanding of the word than mine and neither of us can truly hold power over the word. As for me control doesn't exist in reality because the light bulb doesn't actually control the outcome of the light turning on or off. The beginning of all events is really what controlled the forces to make the force of the light switch going on or off. > Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Yes, I'll take a look at the novel you recommended.
dTal 7y ago
QED. To put it another way, "life" is basically a quine. As per the fixed-point theorem, all Turing-complete formal systems support (infinitely many) quines. Therefore, any universe whose laws of physics are powerful enough to support Turing-completeness, can support life. (Of course you have to be careful with what you mean by "life" and "universe" and so forth. A 0-dimensional infinitesimal singularity capable of arbitrary computation can of course run Conway's Game Of Life all you want - but perhaps you'd prefer 'universe' to mean some kind of spatial construction with locality-preserving rules - in which case it's not even clear that our own universe counts!)
randyrand 7y ago
What is a 1D computer? A computer made with a single line of atoms?
- jolmg 7y ago
  Like another post mentioned, this would be an example: https://en.wikipedia.org/wiki/Rule_110 https://en.wikipedia.org/wiki/Rule_110 Atoms work on 3 dimensions, I believe, and 1D doesn't need to imply our physical 3D existence minus 2 dimensions. It can be a virtual 1D realm that runs on our own defined "physics". The rules that define the "physics" in Rule 110 are: |-----------------+---------------------------| | current pattern | new state for center cell | |-----------------+---------------------------| | 111 | 0 | | 110 | 1 | | 101 | 1 | | 100 | 0 | | 011 | 1 | | 010 | 1 | | 001 | 1 | | 000 | 0 | |-----------------+---------------------------|
AgentME 7y ago
Sure, if your 2D or 1D world is started from a pattern designed by an intelligent being, then they could make a starting pattern that simulated a 3D world. But the more interesting question is whether life could arise in a 2D or 1D world that has simple physics and a simple starting pattern.
deleted 7y ago
[deleted]

> A 2D or 1D computer can simulate life in 3D. Can it? I'm not familiar with the limitations of lower dimensional computation, but it sounds like a fascinating subject.

Will_Parker 7y ago
https://en.wikipedia.org/wiki/Rule_110 https://en.wikipedia.org/wiki/Rule_110 A Turing Complete 1-dimensional cellular automaton. Also Conway's Game of Life is a rabbit hole you could literally spend your whole life studying.
- empath75 7y ago
  That is life like but I would not call it life.
  - jolmg 7y ago
    That's the issue with this question. What is life? Common definitions would never think to consider anything other than things in our 3D physical world. Can Life Exist in 2 and 1 Dimensions? Sure, if we're willing to define "life" generically enough. If not, then no.
  - iso-8859-1 7y ago
    Since the universe may be encoded on lower-dimensional boundary, that means that you are not alive, per your definition: https://en.wikipedia.org/wiki/Holographic_principle https://en.wikipedia.org/wiki/Holographic_principle
jolmg 7y ago
I believe weregiraffe is referring to this[1][2]. Conway's Game of Life is a 2D "world" with 4 rules that define the "physics" in that world, and someone made a Turing Machine in it. [1] https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-Machine-Life.pdf https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-M... [2] http://www.rendell-attic.org/gol/tm.htm http://www.rendell-attic.org/gol/tm.htm
Koshkin 7y ago
One can simulate life using Turing machine.

IanSanders 7y ago

I'd say approximate, not simulate. Or simulate an approximation of 3D. (You need infinite 2D space for a complete model of a finite 3D space)

ralusek 7y ago
Why do you need infinite space? The number line of real numbers is basically a 1d space, and we can simulate finite N dimensional spaces with finite real numbers.
- IanSanders 7y ago
  Let's say you want to represent 1cm*1cm 2d space in 1d. There is infinite number of points in both dimensions of this space. While you can completely represent one of its "slices" with a 1cm segment of 1d space, for a complete model you will need infinite number of 1cm segments stacked, thus requiring infinite 1d space.

jackweirdy 7y ago

Is a simulation of life the same as life?

sysbin 7y ago
Yes. People don't have any real control with what happens in their life. Similar to a computer simulation with 3d objects.
- NickM 7y ago
  People don't have any real control with what happens in their life. Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something. Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Is subjective experience simply a side effect of certain types of computation? That may be true, but if you believe that, you start to get into some profoundly bizarre implications about the nature of reality. Check out the novel "Permutation City" by Greg Egan for a great exploration of this topic.
  - sysbin 7y ago
    > Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something. I disagree with your interpretation of control. The word is human expression and shared between one another. So you can have a different understanding of the word than mine and neither of us can truly hold power over the word. As for me control doesn't exist in reality because the light bulb doesn't actually control the outcome of the light turning on or off. The beginning of all events is really what controlled the forces to make the force of the light switch going on or off. > Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Yes, I'll take a look at the novel you recommended.

dTal 7y ago

QED. To put it another way, "life" is basically a quine. As per the fixed-point theorem, all Turing-complete formal systems support (infinitely many) quines. Therefore, any universe whose laws of physics are powerful enough to support Turing-completeness, can support life. (Of course you have to be careful with what you mean by "life" and "universe" and so forth. A 0-dimensional infinitesimal singularity capable of arbitrary computation can of course run Conway's Game Of Life all you want - but perhaps you'd prefer 'universe' to mean some kind of spatial construction with locality-preserving rules - in which case it's not even clear that our own universe counts!)

randyrand 7y ago

What is a 1D computer? A computer made with a single line of atoms?

jolmg 7y ago
Like another post mentioned, this would be an example: https://en.wikipedia.org/wiki/Rule_110 https://en.wikipedia.org/wiki/Rule_110 Atoms work on 3 dimensions, I believe, and 1D doesn't need to imply our physical 3D existence minus 2 dimensions. It can be a virtual 1D realm that runs on our own defined "physics". The rules that define the "physics" in Rule 110 are: |-----------------+---------------------------| | current pattern | new state for center cell | |-----------------+---------------------------| | 111 | 0 | | 110 | 1 | | 101 | 1 | | 100 | 0 | | 011 | 1 | | 010 | 1 | | 001 | 1 | | 000 | 0 | |-----------------+---------------------------|

AgentME 7y ago

Sure, if your 2D or 1D world is started from a pattern designed by an intelligent being, then they could make a starting pattern that simulated a 3D world. But the more interesting question is whether life could arise in a 2D or 1D world that has simple physics and a simple starting pattern.

deleted 7y ago

[deleted]