What is the Fourth Dimension? (1884)

https://en.wikisource.org/wiki/What_is_the_Fourth_Dimension%3F

by tintinnabula • 5 years ago

68 45 5 years ago

en.wikisource.org

Time is the fourth dimension. Pretty simple.

stevebmark2• 5 years ago

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.

sudosysgen• 5 years ago

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

zamadatix• 5 years ago

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 :)

orangegreen2• 5 years ago

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.

joppy• 5 years ago

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.

brrrrrm• 5 years ago

Time is a fourth dimension.

hgl• 5 years ago

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.

Jun8• 5 years ago

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.

prezjordan• 5 years ago

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

huachimingo• 5 years ago

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

shsbdncudx• 5 years ago

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

karaterobot• 5 years ago

An invisible curve, rising through the centuries.

Drive on, Netley.

RyanShook• 5 years ago

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.

TchoBeer• 5 years ago

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

hpoe• 5 years ago

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?

bombcar• 5 years ago

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).

jimmygrapes• 5 years ago

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.

snomad• 5 years ago

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.

fiddlerwoaroof2• 5 years ago

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_)

saeranv2• 5 years ago

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.

stareatgoats• 5 years ago

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.

intellaughs• 5 years ago

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.

notorandit• 5 years ago

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

thanatos519• 5 years ago

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

goldenkey2• 5 years ago

I recommend the movie too:

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

mentos• 5 years ago

What dimension does thought occupy?

drdeca3• 5 years ago

This does not seem to be a well defined question.

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

emmap212• 5 years ago

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.

ralphc2• 5 years ago

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?

layer8• 5 years ago

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.

goldenkey2• 5 years ago

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.

ralphc2• 5 years ago

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

What is the Fourth Dimension? (1884)

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