3 ms·

I wonder how twisted the author mind is now. He has been working in 4D for more than a decade (first mentions of Miegakure was in 2009), if it is ever possible

by GuB-42 3y ago

I wonder how twisted the author mind is now. He has been working in 4D for more than a decade (first mentions of Miegakure was in 2009), if it is ever possible to get an intuitive feeling of a 4D world, that should do it. The alternative is to just throw away intuition and just do the maths with one extra vector coordinate, but that would be unfortunate for a game that is all about thinking in 4D.

gcr 3y ago
Reminds me of a scene from Schild's Ladder by Greg Egan. This is a conversation between an embodied human and a person who grew up in a completely virtual environment: Yann, sitting beside him, caught his eye. "You okay?" Tchicaya nodded. "In the scapes you grew up in," he asked, "was there a vertical?" "In what sense?" "I know you said once that you didn't feel gravity...but was everything laid out and connected like it is on land? Or was it all isotropically three-dimensional--like a zero-gee space habitat, where everything can connect in any direction?" Yann replied affably, "My earliest memories are of CP4--that's a Kähler manifold that looks locally like a vector space with four complex dimensions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this"--he motioned at the surrounding, more-or-less-Euclidean space--"for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate, visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single, three-dimensional space." So much for being a seasoned traveler. Tchicaya didn't envy Yann's upbringing, but it probably rendered the world behind the border less exotic to him than the notion of a jungle had been to Tchicaya as a child. It shook his confidence to be reminded that there were measures by which his millennia of experience had been laughably narrow.
rcme 3y ago
The 4th dimension is somewhat intuitive if you think about it like a 3D space + a time dimension.
- jasonjmcghee 3y ago
  Personally, I don't agree with this. I can't grasp the concept of 3D by only thinking in 2D + time. I find a more effective attempt at imagining 4D space to consider what it would be like to only see in 1D projection of 2D space. Imagine standing on a piece of paper with other pieces of paper sitting on top that create a maze - all you can see as you turn and move about in 2D space are where walls and hallways are. You have a concept of depth (in 2D). You can move about the maze. Now imagine the sensation of that flat world expanding into 3D space and your senses expanding with it. Now it's a 3D maze and you can fly- able to navigate the 3D space. That change you just imagined, try imagining that same expansion into a fourth spatial dimension and it being projected into a 3D space you can perceive. Instead of being able to tell the 3D shape of something by observing shading and how light interacts with it, you'd be able to perceive the 4D shape of something, even though you can only see a 3D projection at any given time.
  - rcme 3y ago
    How I use time to visualize the 4th dimension is this: Imagine standing on one side of a room at t0 and walking across the room, reaching the other side at t1. At each instant in time, your body has a 3D position in the room. So the 4D shape of your body between t0 and t1 is kind of like the path your body took through the room. You can create a 3D slice at any point between t0 and t1 and get exactly where your body was at that moment in time.
    - jasonjmcghee 3y ago
      For the sake of discussion let's try it for 2D->3D: At each instant in time, your body has a 2D position on the screen. So the 3D shape of your body between t0 and t1 is kind of like the path your body took across the screen. You can create a 2D slice at any point between t0 and t1 and get exactly where your body was at that moment in time. That doesn't help me understand 3D space. It helps me understand 2D changing over time. Think of all the implications that "depth" - that extra spacial dimension - has on the world. How dramatically it changes things, and how differently things work with it.
cubefox 3y ago
I'm pretty sure our brains are hardwired to perceive euclidean 3D space as a perspective projection onto our 2D retinas. We can only understand 4D space in an intellectual, non-intuituve fashion.
- BossingAround 3y ago
  I think you'd be surprised how much our perspective can change. I'm not sure we can understand 4D, but I'm definitely sure we can think we intuitively grasp 4D.
- barrysteve 3y ago
  It's not that hard. Play with 4D toys and several intuitions jump to mind. the slices of dimensions from one d dot to four d object make sense when you roll them around in your hands via game controls. Space Dandy had an episode where the hero dates a four dimensional girlfriend. It's not 'magic', it makes sense. The idea that our brains are hard wired for basic concepts is almost synonomous with a self-limiting belief. There needs to be a lot of hard evidence/definitive causation, to make those claims about a biological organ and not accidently limit yourself.

by GuB-42 3y ago

gcr 3y ago

Reminds me of a scene from Schild's Ladder by Greg Egan. This is a conversation between an embodied human and a person who grew up in a completely virtual environment: Yann, sitting beside him, caught his eye. "You okay?" Tchicaya nodded. "In the scapes you grew up in," he asked, "was there a vertical?" "In what sense?" "I know you said once that you didn't feel gravity...but was everything laid out and connected like it is on land? Or was it all isotropically three-dimensional--like a zero-gee space habitat, where everything can connect in any direction?" Yann replied affably, "My earliest memories are of CP4--that's a Kähler manifold that looks locally like a vector space with four complex dimensions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this"--he motioned at the surrounding, more-or-less-Euclidean space--"for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate, visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single, three-dimensional space." So much for being a seasoned traveler. Tchicaya didn't envy Yann's upbringing, but it probably rendered the world behind the border less exotic to him than the notion of a jungle had been to Tchicaya as a child. It shook his confidence to be reminded that there were measures by which his millennia of experience had been laughably narrow.

rcme 3y ago

The 4th dimension is somewhat intuitive if you think about it like a 3D space + a time dimension.

jasonjmcghee 3y ago
Personally, I don't agree with this. I can't grasp the concept of 3D by only thinking in 2D + time. I find a more effective attempt at imagining 4D space to consider what it would be like to only see in 1D projection of 2D space. Imagine standing on a piece of paper with other pieces of paper sitting on top that create a maze - all you can see as you turn and move about in 2D space are where walls and hallways are. You have a concept of depth (in 2D). You can move about the maze. Now imagine the sensation of that flat world expanding into 3D space and your senses expanding with it. Now it's a 3D maze and you can fly- able to navigate the 3D space. That change you just imagined, try imagining that same expansion into a fourth spatial dimension and it being projected into a 3D space you can perceive. Instead of being able to tell the 3D shape of something by observing shading and how light interacts with it, you'd be able to perceive the 4D shape of something, even though you can only see a 3D projection at any given time.
- rcme 3y ago
  How I use time to visualize the 4th dimension is this: Imagine standing on one side of a room at t0 and walking across the room, reaching the other side at t1. At each instant in time, your body has a 3D position in the room. So the 4D shape of your body between t0 and t1 is kind of like the path your body took through the room. You can create a 3D slice at any point between t0 and t1 and get exactly where your body was at that moment in time.
  - jasonjmcghee 3y ago
    For the sake of discussion let's try it for 2D->3D: At each instant in time, your body has a 2D position on the screen. So the 3D shape of your body between t0 and t1 is kind of like the path your body took across the screen. You can create a 2D slice at any point between t0 and t1 and get exactly where your body was at that moment in time. That doesn't help me understand 3D space. It helps me understand 2D changing over time. Think of all the implications that "depth" - that extra spacial dimension - has on the world. How dramatically it changes things, and how differently things work with it.

cubefox 3y ago

I'm pretty sure our brains are hardwired to perceive euclidean 3D space as a perspective projection onto our 2D retinas. We can only understand 4D space in an intellectual, non-intuituve fashion.

BossingAround 3y ago
I think you'd be surprised how much our perspective can change. I'm not sure we can understand 4D, but I'm definitely sure we can think we intuitively grasp 4D.
barrysteve 3y ago
It's not that hard. Play with 4D toys and several intuitions jump to mind. the slices of dimensions from one d dot to four d object make sense when you roll them around in your hands via game controls. Space Dandy had an episode where the hero dates a four dimensional girlfriend. It's not 'magic', it makes sense. The idea that our brains are hard wired for basic concepts is almost synonomous with a self-limiting belief. There needs to be a lot of hard evidence/definitive causation, to make those claims about a biological organ and not accidently limit yourself.