I never said it wasn’t. But Beethoven could imagine and write the 9th. Now tell me that that is an order of magnitude easier.
I disagree. Beethoven was extraordinarily gifted with a sense he already had, at least for most of his life. Imagining what things sound like isn’t quite so hard when you actually have or have had a sense of hearing. I can’t look at a score and hear the entire orchestra in my head, but I can look at a single instrument’s piece and have an idea what theirs sounds like. 4D is a sense we’re completely lacking. I can imagine a 4D shape as a series of 3D shapes, and perhaps some people can carry that a step further, but saying they can actually visualize the shape in their mind as if they had a 4D eye is like someone saying they could visualize what our world would look like as a tetrachromat. It’s something I need proof to believe.
A 3D line that exists through all time is a hyperplane. Get it? One dimension is, say, the X-axis. The other is time.
The line could be flying. That would be a hyperplane at an angle. The line could be rotating. That would be a complex shape.
I can project the hyperplane down into 3D by giving the line motion trails (instead of leaving it as is), but I still have a very good distinction in my head between the time-based nature of motion trails and the line wearing an actual little cape. I can also imagine two such lines flying around. These are skewed hyperplanes. But, if by some rare chance (and it is a rare chance that hyperplanes intersect), that the flying lines cross eachother, then that is two hyperplanes intersecting at a point.
Rotating cubes through time is similar. One point exists two minutes ago, with the others existing later. At each moment in time during which the (still 3D) cube exists, it looks like a 2D cross-section. Literally, all you do is scatter 2D cross-sections of a cube through time. And a hypercube? The cross-sections are 3D. Duh!
What Chronos did is remarkable. Mostly because he did it all in his imagination.
Since today we have access to software, it should be much easier to gain his abilities by simply watching and manipulating. Will still take a while, but it should be easy enough even for an adult. Which is why I was asking where one could find it. (If it really doesn’t exist, or it’s all crappy Java, then it’d be trivial to program something in Direct3D. Add in Nvidia’s stereoscopic tech, and it gets quite a bit better.)
Interesting add-on: If we imagine a cube with sides of length 1 foot, and we rotate it into time, we can say exactly how far apart the sides are: one nanosecond. Physics tells us this.
Also, I think I was mistaken in saying that when infinite lines fly, they have a slim chance of crossing. Actually, I think they almost always will. But, they have a slim chance of making anything but a point when they do. Hence, most hyperplanes cross at points.
Four-dimensional beings could have eyes that see in 2D, and they would still be able to live and function. If you accused them of being horribly crippled compared to beings with 3D eyes (which may very well be a fair characterization), they’d punch you in the nose and call you a biggot.
In the land of the [3D] blind, the man with the one 1D eye is still king. (1D eye = take an imagine and smear all the vertical pixels.) He just has to rotate his head a lot.
One of the most interesting talks I’ve been to was given by Dmitri Tymoczko, who gave a presentation on his modern geometric view of music theory. As part of this talk, he displayed a mapping from the circle of fifths to a four-dimensional structure in which consonant chords are represented by adjacent points. To demonstrate the utility of this notion, he played an animation that showed the path taken by the chords in a piece by (IIRC) Schubert that has defied analysis by traditional theory. It was immediately obvious that the composer had an intuitive understanding of this structure. I have no idea whether he could visualize it, but it’s not clear that that’s important.
We can’t visualize it or represent it “as it actually is” since, insofar as we do not visually perceive it, there IS no “as it actually (visually) is”. But we can represent it easily enough.
Easy way: just steal color. In your diagram or representation color will cease to stand for itself (thus, whatever is represented will be understood to be lacking actual color information) then use the spectrum from the violet end to the red end to represent a “W” axis.
Color will really only get you the surface of your object, though, not the entire interior. If a pixel is, say, green, that only tells you about that pixel, not any blue pixel that might be “behind” it.
And for the doubters, why is it any more fundamentally remarkable that a person could visualize four dimensions than it is that one could visualize three? We can’t actually see either with our eyes. But nobody finds it so remarkable that our brains are able to construct 3D visualizations from the 2D images our eyes give us. Given that most people can do that, why wouldn’t some folks be able to take it further?
I can’t refute your experience, only answer your question from my point of view. The only reason my brain is able to take 2D data and create a 3D model is that I actually live in 3D. I can move about in three dimensions and correlate that experience to the 2D data that my brain is getting, creating a seamless 3D model of my world.
But I have no experience on which to base a 4D model, just mathematical concepts. My brain just can’t do it. Doesn’t mean yours can’t.
Chronos, what’s a good jumping off point? Meditating on two planes meeting in a single point? Thinking about a ‘surface’ of a 4-d object being a 3-dimensional thing? Imagining 3-dimensional slices of 4-d objects? How do you get there?
I’ve wondered something similar myself. Why couldn’t our brains construct a 4-D perception ‘in the mind’s eye’, even if we don’t have any sense organs in a 4-D space? Then I got to wondering, what whith the new techniques of brain stimulation, could we construct something that would feed synthesized 4-D imagery to the brain?
Are you saying we currently have the technology to electronically put an image in someone’s head? I must’ve missed this.
Combine optigenetics with eye implants with brain-to-brain communication via the internet, and it seems to me that we’re getting close/. I think that we may be able to put something into the brain that could be interpreted as a perception of a four-dimensional object. Perhaps, as in animation, it would be its topology and motion that would help to establish its 4-D properties, rather than its direct appearance.
Here’s a 4D maze game:
http://www.urticator.net/maze/download.html
I suspect enough practice with this may get you there, but the author said:
Not really. This so-called brain-to-brain sends exactly one bit of information. It carries no additional information in any form. As an example - here is a bit for you. Care to tell me what I was thinking about?
1
The bit in the article is created by training both the sender and the sensors to find a mutually useful way of 1. thinking, and 2. sensing the broad brush electrical patterns on the scalp. Secondly, the impulse is not deliverd back to the recipients brain in a symmetric manner. They don’t get a similar sensation induced into their head. They just get a bit. Maybe on a screen - just like the one above. This less brain-to-brain communication than Morse code.
The problem with any idea of brain to brain outlines one of the issues touched on in this discussion. Our individual brains are actually wired differently. We have no idea what happens in our heads to represent complex (or even simple) information, but we are pretty certain that different people can process different types of information, and that some people simply can’t manage things that others find inate (and vice versa.) If Chronos visualises a 4D space, it is very unlikey that someone who has not developed the same skills could in any manner be in a position to map the information structures in Chronos’ brain to their own. The firmware would actually be missing. The area of brain Chronos uses to visualise 4D would have been wired for a different purpose in another person’s brain. So it would be about as useful as trying to run a computer program compiled for a x86 on an ARM.
For common aspects of human thought there may well be enough commonality that (in principle) a mapping between brains can be created. But for the really hairy special capabilities, no hope, and it is very possible that there is significant variation even for more simple tasks. All we know is that the brain learns to do stuff. But the internal information represenations are utterly opaque to us. We have a tiny tiny idea of how capabilities for trivial functions might work from our knowledge of computational neural networks. But one of the essentially impossible things to try is to reverse engineer what a neural network is doing for all but the simplest.
Why are all these programs made in shitty Java! Look at it, it’s done in 70s style wireframe. The kind where you don’t know what’s going on even if it’s just 3D. No wonder it hasn’t helped its author achieve his goals.
If noone’s really done this, maybe I’ll write it up myself. It’s trivial to use the programmable GPU pipeline to render 4D models instead of 3D, and they can be all pretty, shaded, and realistic. The trick is figuring out what interaction to have. I think rotation is the most difficult to understand. Projecting 4D into 3D is also tricky. Moving linearly through cross-sections would be easiest. Maybe it can start off with animated explanations of some concepts (like the flying lines I tried to explain), and progress through the different levels.
I would also make it stereoscopic (like this Java example). But I wonder… what if the parallax happens in the 4th dimension. Can our brains ever adjust to that? Can a baby’s?
Yeah, I love the idea of the app, but I agree it’d be eye-hurting even in 3-d.
Besides that, the keys that control movement are…not intuitive, shall we say.
As for eating/digestion…this isn’t my idea but cannot remember who came up with it. Yes…A digestive track would cut a 2d creature in half…however it could have ‘hooks’ all along the digestive track and when food passes through it would unhook allow the food through and rehook. Gives a horror to realize there could be a disease that affects the hooks causing them to unhook and the creature breaks in half and all his insides pore out.
As for the railroad…no. Flatland is not a good representation of 2-D space. If you want to make it look like ours…planets would be large circles which creature would walk on the surface. This means they could only move forward/backward. If such a universe exists with life…I imagine they would need the 2 degrees of movement so ‘flying’ would be important.
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I remember reading that hypersphere planets orbiting a hypersphere star do not have stable orbits…so there is a reason we might be in a 3 spatial dimension universe as life may not be possible in 4-d.
Is the stability thing true?