What is the Fourth Dimension? (1884) | Hacker News Reader

What is the Fourth Dimension? (1884)

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68 pointstintinnabula45 comments

Talk about a family who was familiar with the fourth dimension! Charles Hinton, author of this interesting essay, married Mary Ellen, daughter of Mary Everest Boole and George Boole. Mary Ellen's sister, Alicia Boole Stott (http://www.ams.org/publicoutreach/feature-column/fcarc-boole) "was first exposed to geometric models by her brother-in-law Charles Howard Hinton when she was 17, and developed the ability to visualise in a fourth dimension." She invented the word polytope.

Charles Hinton was quite the inventor, he first set up a 3D grid of rods for children to play in and develop Cartesian thinking; this became the jungle gym, which his son, Sebastian, patented. He also invented a gunpowder powered pitching machine to train baseball players (https://www.atticpaper.com/proddetail.php?prod=1897-charles-...), after causing more than a few injuries had to be retired.

He's the great-grandfather of Geoffrey Hinton.

In his book The Fourth Dimension (https://archive.org/details/fourthdimension00hintarch) he shows how to build models for one to think in 4D, starting on pg. 230.

I would hate to be at the same bar as you on trivia night. Thanks for this comment - this is unbelievably interesting.

I still remember the first time when I saw videos about non-Euclidian Geometry[1] and Higher Dimensions[2]. I was amazed with such concepts, but I still havent read books about them. They are related somehow with topology[3] and curvature (and tangentially, to differential equations).

[1]https://youtu.be/n7GYYerlQWs (5 sided square)

[2]https://youtu.be/4TI1onWI_IM (The road to 4D part 1) https://youtu.be/N0WjV6MmCyM (Carl Sagan's explanation)

[3]https://youtu.be/lmcT2mP2bfE (Zach Star's intro)

Also, a nice exercise to visualize 4D is to study quaternions and their properties. Vectors are somehow a nice simplification of them, see Maxwell laws. 3blue1brown has a video[4].

[4] https://youtu.be/d4EgbgTm0Bg

For anyone who is not extremely scientifically literate in regards to quantum physics, the kid in this video (https://www.youtube.com/watch?v=eGguwYPC32I) explains the 4th dimension in an extremely comprehensible way. I first came across it about 4 years ago and have probably watched it 20 times since.

This brings me to "Flatland" by Edwin Abbott Abbott published the very same year. https://en.m.wikipedia.org/wiki/Flatland

For a working out of how things like homes and steam engines and boats might work in a 2D world: https://en.wikipedia.org/wiki/The_Planiverse

I recommend the movie too:

https://en.wikipedia.org/wiki/Flatland_(2007_film)

If we assume the world is a cube, I would think of 4D as a several projections of 3D cubes in another 3D cube. For higher dimension, I find myself in algebraic topology. This is really tortuous to think of these concepts.

Ever since reading Time-Life books in the library in the 70s I've wanted to visualize the 4th dimension. Has anyone actually achieved this? And if someone claimed to, how would we verify it?

You can visualize 4D objects by visualizing morphing 3D objects (i.e. use time as the 4th dimension). Where it becomes tricky is 4D rotation, but I suspect that after a while you can get some limited intuition for it.

Now I wonder whether it couldn’t also be visualized as the cross-product of two 2D worlds. We have two eyes with a 2D retina each, so maybe they could be trained for that. 4D obviously requires more representational space in our brain than 3D, and the per-eye visual processing apparatus would be limited to the respective pair of dimensions, so the internal visualization will probably have to be more coarse-grained or blurry in some way.

It's really not difficult if you just consider what a dimension really represents...a degree of freedom. So a 4th spatial dimension for us would be as if each point in our 3d space had a hole at the center of it. The 4th dimension is inside of every point. Lets say this 4th dimension is not infinite and is only 1 meter long. Then each of these holes would be 1 meter deep. The 4th dimension is just the result of replacing each point in 3d space with a line.

If you start with a point, and you recursively replace all points (not just endpoints), with perpendicular lines (no overlap with existing points), you'll have a simple process that constructs higher and higher dimensions.

It's possible that gravity originates from a 4th spatial dimension and thus appears to be radiating outward isotropicly from the center of all matter.

Reminds me of Flatland.

I always get confused when some refer to time as the fourth dimension when there seem to be many more spatial dimensions than just the first three.

The problem here is "fourth" as if dimensions can be ordered. Time is a dimension, and together with three spacial dimensions that makes 4.

It is very possible that I just don't understand but when I was studying ML and learning a little bit about the math behind it I suddenly realized that in one sense the word "dimension" simply means a value required to identify the location of a point. The number of dimensions requires indicates the number of values required to distinctly identify a point. For example in 2 dimensions it requires only 2 values or data, x and y, to uniquely identify a point. In 3 dimensions x, y and z, etc.

Now visualizing them can become much more tricky but mathematically we can still describe them.

Thus to bring it to your point about time as the fourth dimension if you want to ask your friend to meet you for lunch in the empire state building, you would have to give him the longtotude and latitude of the Empire State building (x and y) the floor to meet you on (third dimension z) but you would also have to give him the time to meet you, time being the 4th data point and ergo the 4th dimension.

Honestly what confuses me is what special distinction does time get to make it not considered a dimension like the others?

Time is the only dimension we can’t control travel on - we’re stuck at 60 minutes an hour. So it doesn’t exactly map the same way the others do (though arguably all the first three are only analogous to the real world, as points and lines and planes don’t exist as non-3D objects we can interact with).

You are entirely correct about how time should be thought of as just another point of reference. The reason I think it is viewed as the "4th dimension" is because it's something we can naturally observe without any tools.

> Honestly what confuses me is what special distinction does time get to make it not considered a dimension like the others?

My less-than-a-layman understanding is that it really is just a physical point/plane - but as 3-dimensional creatures it will appear to us as time.

Sagan's flatland video shows the 3-d apple moving through 2-dimensional as transitory slices; the 2-d creatures don't see the entire apple because they are fine tuned for 2-d existence.

Interesting, but this seems to contradict(?) the fact that there are 4+ spatial dimensions.

This reminds me of passage in a book or movie (can't remember which one) which talked about the idea of human beings in 4D as worms, with the tail of the worm being the baby, and the face being our current state. As we go through life we keep elongating the work and overlap ourselves in space.

Mr. Nobody?

There’s a Heinlein short story with a similar passage. It’s in a compendium of stories called The Man Who Sold The Moon.

One weird thing about time is that it’s sign is “flipped” in the spacetime distance equation. So, while in some sense it’s “just another dimension”, it behaves somewhat differently from the spatial dimensions when measuring distance.

(I’m not an expert, just remembering something I found interesting in Einstein’s book _Relativity_)

For what happens if the sign is NOT flipped, see https://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html#CC

This is a really cool sort of science fiction: attempting to build a story around a world where some fundamental scientific law has been adjusted.

One thing is that we can only move forward in time. I have always heard the second law of thermodynamics (entropy always increases) defines the "arrow of time": you cannot go back to a previous ordered state unless you add work, thus you are forced to march forward in time.

Is entropy The Langoliers?

My hunch which is that the term "dimension" is an example of overloading a word which originally simply meant the three coordinates required to describe a point in traditional Euclidian space. With the introduction of the fourth 'dimension' (time) the floodgates broke open and with mathematics in the lead any attribute can now be said to be a dimension. For people still holding on to (and valuing) the original meaning it becomes confusing.

Case in point is the star schema of traditional data warehouses: there is no end to the number of 'dimensions' that a fact may have. But they are really just attributes. Same could be said of dimensions in mathematic; they simply denote attributes, albeit in somewhat 'spatial-like' domains.

Time to mention miegakure, a 4d puzzle game that will be done "when it's done" https://miegakure.com/

What dimension does thought occupy?

This does not seem to be a well defined question.

What do you mean?/What are you trying to ask?

An invisible curve, rising through the centuries.

Drive on, Netley.

Electromagnetism is the 4th dimension, that’s why we are bound by the speed of light, as every dimension is bound by those below it

Time is the fourth dimension. Pretty simple.

I always find it irksome when people call time the "fourth dimension." Time is not related to spatial dimensions, and claiming this shows a lack of understanding about the concept of higher spatial dimensions.

Time certainly isn't a fourth spatial dimension, but you can imagine if it was.

Time is very much a dimension inextricably related to the spatial dimensions (and vice versa) in reality so arguably one should find it irksome when the topic of a 4th spatial dimension isn't fully qualified instead of the other way around.

I think that can be forgiven in 1884 though :)

0th dimension: a point in space

1st dimension: a line in space

2nd dimension: a plane in space

3rd dimension: an object with mass (width, height and length), represented as a point in time

4th dimension: a time line, where the third dimension can travel on

5th dimension: a time plane, representing the events of infinite time lines.

6th dimension: third dimensional time space, which, honestly, gets kinda confusing, but I'm pretty sure it has something to do with the infinite possibilities of time planes. As in, time planes have time lines that actually happen, but 3d time space are what could happen? I'm not entirely sure.

And on and on. My visualization of dimensions is that it infinitely repeats itself based on point, line, and plane.

No, this is wrong/nonsense. I assume you got this from that one YouTube video? The one with the white background and animated black lines, claiming to explain 12 dimensions?

Learn basic linear algebra to get the idea of the dimension of vector space. Then maybe learn a bit about the box counting dimension or similar for fractals as another related notion (which allows non-integer values).

Speaking about dimensions without doing math is a mistake.

You seem nice.

I didn’t insult them.

I just told them to learn some things which are entirely within their capability to learn, so that they can think about the topic they were talking about, without thinking nonsense.

It shouldn’t take more than a couple hours (possibly under an hour to get the ideas I was referring to), and knowing basic linear algebra is good for a person.

If I was blunt, it is because I dislike misinformation, and highly value mathematics. Perhaps I’ve even warped my view of things in a way that makes me feel that someone understanding mathematics is a terminal moral good? Which, if so, is probably an error on my part.

You might want to look at Simplex to describe better and more rigorously. Simplex is the most basic structure to describe a space in n-dimension.

0-simplex: a point.

1-simplex: a segment (points and lines)

2-simplex: a rectangle (points, lines, and surfaces)

3-simplex: a tedrahedron (points, lines, surface and a 3D space that most of human can comprehend visually)

4-simplex: everything above and the whole combination of these element in algebra.

This is how mathematician and physicists solve problems. Time is a separate element in our equations that why we often talk space-time, not just space

https://en.wikipedia.org/wiki/Simplex

No, you can't extrapolate time dimensions like you can extrapolate spatial dimensions. This smells like "Imagining the 10th Dimension," which is hilariously bad if you haven't seen it.

The whole point of special/general relativity (at least the Minkowski approach to it, ie the approach that calls time a dimension) is that it the time dimension is related to the spatial dimensions. At non-relativistic speeds it seems unrelated, but for very fast-moving objects or particles the interplay between space and time becomes quite important, and for an object moving along a path the notions of time as-measured-by an external observer (roughly, ending coordinate in the time dimension minus the starting coordinate) and time as-measured-by the object (roughly, the Minkowski-length of a path in spacetime) become quite different things.

This just made me realize that the example given in the article of a 3D framework of strings interacting with a 2d plane would have its own speed limit since the fastest a point created by a string could move would be the case where the string was almost parallel to the plane. It would also stretch the moving point along its axis of movement approaching infinity the closer it got to being parallel. That thought experiment seems even more profound than it initially did. I wish I knew more physics.

Time is a fourth dimension.

This is akin to 2D beings saying time is the third dimension and being satisfied with the conclusion and happily living in their 2D world.

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