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What are your imaginative ways of thinking of multiple dimensions?

One - line
Two - plane
Three - space
Four - spaces along a line
Five - spaces on a plane
Six - spaces in a space
Seven - spaces in spaces along a line
Eight - parallel to five, and so on...

When I try to imagine it, four can be a space along the time axis. Five can be, time axes in multiple universes. From six onward I move to a Russian doll style imagining, encapsulating spaces and zooming out, and it turns fractal.

@daylen? @7w5? Anyone?

I usually get mired down between 3 and 4 puzzled about matters such as probability, relativity, entropy, complexity, and information.

I’m a timid driver, so I sometimes comfort myself when taking turn into traffic with thought that my consciousness will only continue in a universe where I survive.

Also, I tend to easily wander from math into biology and narrative. As space opens towards the future, the improbability of the existence of a tiger becomes the great likelihood of its extinction, yet who might win the next presidential election remains unknown. Why?

I never understood why people put in time as another dimension.

I find these things are easier to understand if you set one of your spatial variables to a constant. This is basically how something like a three dimensional surface on a topo map can be seen as a series of 2d contour lines. So by establishing a level set function of dimension N-1 for a function with N dimensions you can at least visualize 4 dimensions as a series of volumes in 3D.

To get past 4 you need to close your eyes and use the math. I guess we are kind of limited as humans in how we perceive reality. But if you just trust the equations you can represent 5,6,7 dimensions abstractly. We do it all the time when data has more than three variables. Actuarial relationships between mortality, diet, driving laws, disease rate, locale etc. can be seen as N space abstractions.

There was a book called something like Flat Land or Line World that was always recommended to me by physicists. Anyone remember that thing? I never read it but it is supposed to be about a world that exists on a line and he it looks to outside observers.

I've lost track of how many dimensions I am in.

Depends on how concrete a definition you are working with for dimension. In a loose form, a dimension may just be a frame (circle or line segment) that can be fitted with a point. Multiple frames or dimensions are independent if each can be fitted without altering the fits on other frames. Varying a fit may reveal a dependence on some other fit, indicating a correlation. If these frames cannot be untangled, then they may be treated as causal whereby a B is conjured in the form ( A -> B -> C )... just Be-cause.

@sclass
https://en.m.wikipedia.org/wiki/Flatland

@gp I deal with multidimensional issues in doing stats work. You can add in colors and textures to graphs to add more dimensional it’s sometime. My question would be why are you trying to conceptualize extra dimensions. OTOH for physics type stuff my mind just goes to mush even dealing with real world 3 d

@7w5 I'll say it to myself the next time I am behind the steering wheel.

@Sclass, I would bet that time coming to mind as the fourth dimension has to do with the Western tradition of thinking about time as past-present-future. I get what you mean with visualising 4 dimensions as a series of 3D volumes, making stop motion pictures come to mind. I will read the Flatland book if this is still on my mind in some time.

@daylen now I have another imaginative way of thinking about multiple dimensions in the form of an audio mixer sound console.

guitarplayer wrote: ↑

Sat Jul 10, 2021 2:51 pm

@Sclass, I would bet that time coming to mind as the fourth dimension has to do with the Western tradition of thinking about time as past-present-future.

What? Wait, I thought that was from the Twilight Zone intro.

I like the color plot analogy. You can have a three dimensional surface or volume that is colored at each location with 256 bit color and that gives our primitive minds a way to see four dimensions. A three dimensional heat map is a visualization of 4D.

Many years ago I listened to this Russian expert on the multiverse (or it’s laughable non existence) and he said some interesting things. One he said that we perceive our universe the way we do because we evolved in its physics. The second thing he said is that in the infinite number of possible parallel universes there will be multidimensional realities with beings that can perceive and live in them because they evolved in N dimensions. I’ll have to look up the guy’s name. It was interesting but he warned us that there was no way to prove or disprove anything he was saying.

ETA- looked him up. Andrei Linde. He has some Youtube videos. Fun to listen to.

Sclass wrote: ↑

Sat Jul 10, 2021 4:13 pm

I like the color plot analogy. You can have a three dimensional surface or volume that is colored at each location with 256 bit color and that gives our primitive minds a way to see four dimensions. A three dimensional heat map is a visualization of 4D.

This is good in principle but for mildly colour blind doesn't stick much.

Yeah my thinking is tinted by the spacial dimensions framework. Thinking longer about it, anything distinguishable from its environment can be considered a dimension, even if only a binary one.

Playing 5-d games is a fun way to build up this skill.

Our earing is one dimensional, our vision bidimensional. Our World is apparently tridimensional, but we see it trough projection on lesser dimensional spaces. A more dimensional World could also bé projected on lesser dimensional Space. So to imagine a more dimensional World, i picture how it would project on a lesser dimensional Space. I'm pretty sure thé human brain could handle it easily with our current sensés, if exposed to a more dimensional World for a few days.
So it's quite similar to what sclass does.

So the way I see it can be represented as below:



The first three dimensions are the dimensions of the smallest cubes.
* The smallest cubes should be throughout but I have drawn only eight in the bottom left corner so it is not cluttered.
* You have to imagine each of the edges of each of the cube to contain the real line i.e. go from minus infinity to plus infinity. This is counterintuitive because the edges are bounded, think of infinity in the sense of Zeno's paradox.
* Edges consist of infinitely many points.

The 4-th, 5-th and 6-th dimension, these follow the same principles as above, but with the edges of the second cube being 'thick' i.e. consisting of cubes and not points any more. You can think of it as an infinite wall of bricks that is infinitely thick. Each brick has the properties of the cube above.

The same follows for each following three dimensions.

Imagine trying to turn yourself inside-out but ending (or not ending?) up with a hyperbolic plane of mechanized elves. Jokes.. they are really remnant cellular automata from ancient body plans dancing out to the horizon.