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Comment by vpmadd52huq | Hacker News Reader

I've always wondered why humans seem to be unable to visualize four-dimensional objects in their heads.

When discussing this with others, the arguments often revolve around the fact that as we experience our reality in 3D, there should be no reason for us to be able to visualize anything in a higher dimension.

This argument seems like an arbitrary limitation of the human mind, which I don't think holds up. It is sometimes associated with our inability to think of new colors, but I think this is a completely different problem.

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I think thats a pretty simple answer; when was the last time you interacted with a 4th dimensional object be it representation or not? For the most part I think people base their perception of reality on their experience and so if you have never interacted with something, how could you imagin it?

Reminds me of this youtube video I saw some time ago of someone that posed the question of what would minecraft be like if it was in non-euclidean space. The author said it took some time to get used to it and when they tried to play normal minecraft it gave them motion sickness.

If you have no knowledge of what a car is or its internals are like, could you still imagin what's inside?

Exactly, maybe spend a fraction of (the time you spent interacting with 3D objects) interacting with 4D objects and you might find it much easier.

The idea of embodied cognition might explain why we struggle to intuitively visualise objects in four-dimensional space. Basically the argument is that our visual imagination is grounded in sensorimotor systems that are optimised for three spatial dimensions. But reasoning is not limited to sensory experience so we can abstractly figure out how spatial systems in higher dimensions would work if they actually existed. Like we do for most mathematical concepts that don't easily map to what our bodies experience.

So by this perspective, it's not arbitrary, but is the result of our physical embodiment and how we interact with the world.

"This argument seems like an arbitrary limitation of the human mind, which I don't think holds up. "

And why not?

Evolution did not reward us for thinking about spaced out concepts, but for coming up with new ways to get food, outsmart the prey, build tools.

That thinking in 4D is helpful for building tools is a new thing so we evolution did not optmized for it (yet).

Most of our thinking now is about how we made rocks think, gods, and fiction. None of those are created by evolution

Yes, we've managed to make our ancient hardware run more modern software but it's a bit of a kludge and causes compatibility issues.

Are you sure we can't visualize 4D objects? Or rather, what exactly does that mean?

Can we visualize 3D objects? Or do we reason about 3D objects, but only visualize a 2D projection of 2D boundary surfaces embedded in 3D space? I'm definitely not thinking about the inside of my desk lamp, or even its back side, even though those are as much a part of the 3D object as the front surface.

Can you visualize a 1D projection of a 2D object? Probably, but is it a little tricky? How about a 1D projection of a 3D object? And when that 3D object moves? How about a 2D projection of a 3D object, but seen from the inside out with a Hammer retroazimuthal projection, instead of viewed from a distance with the embodied camera eye and wonderfully simple rectilinear(ish) projections that we're so familiar with?

Arguably, I think we can visualize 4D objects. They just look the same as 3D objects, because the visualization is itself a 2D projection. If they move, they look like wobbly 3D objects, as we pick up a different "slice" or "surface".

Now, we don't know very many 4D shapes, because we don't encounter them in our lives. But I think that's fully explained by familiarity, without invoking the idea of an arbitrary limitation. We've all seen lines, sheets, boxes, balls, pyramids— Try describing to a random stranger what a Strandbeest or a Klein bottle looks like.`

The only reason we can’t fly is that we don’t have wings.

It’s a limitation created by our brains evolving to process 3D environments. If we were LLMs we have no 4D training data.

A great example is the film Arrival.

Arrival is one of the best films ever.

> It is sometimes associated with our inability to think of new colors, but I think this is a completely different problem.

As an aside, thinking of a new color is relatively easy. You can sorta actually see new colors just by making a really good pigment[0], or shooting cone cells with lasers[1].

But there's also the possibility of having a new photoreceptor. In which case, you don't just gain 1 new color. You gain 3 new secondary colors, plus an entire new type of 4 "tertiary colors", each of which is as visually distinct as cyan, magenta, and yellow are. And the colorspace itself becomes a 4-dimensional volume, with every existing color able to blend into smooth graduations of the new cone cell signal.

[0] https://www.youtube.com/watch?v=_NzVmtbPOrM [1] https://en.wikipedia.org/wiki/Olo_(color)

People can solve a 4D Rubicks cube, so some parts are possible I guess.

I can think of new colors, but I don't have a way to relate them to stimuli I've experienced, which makes it difficult to make sense of them the same way I can recall seeing existing colors. Still, I and many others have a notion of color that encompasses more than what my eyes can actually see, and I even have some friends that see much, much more in terms of color (such as texture, sensation, etc.)

https://en.wikipedia.org/wiki/Olo_(color)

Our 3D visualization relies havily on photons doing the heavy lifting of traversing 3D space in straight lines, people get, you know, accustomed to it. In fact how we see things is frozen by physics, not brains - they are just accommodated to reality

There are no such utility particles doing any heavy lifting in 4D, so nothing to accommodate to.

I think the idea is that the geometry of straight lines in 4D should be similar enough to picture using the same mental abilities.

How we see is frozen by not only physics, but also biology. We can't actually see in 3D, only in the 2D of our retinae (and the embedded 2D of light-exposed surfaces). That's true for both 3D and 4D objects. I suppose fish, with their electroreceptive abilities, might be the only animals that can sorta "see" in true, volumetric 3D.

biology plays the role, certainly, but nature was trying to capture a model for 3D physical interactions first of all, physics first. And final choice of two 2D sensors is explicitly optimal and minimally effective for 3D - so it can not be similarly descriptive for 4D, just not fair to expect results on same level imho.

For meaningful 4D perception on similar level our body need three volumetric sensors, separated, to define volume with 4D direction

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