4th dimension - Page 2

[Stuugie]

Ya but not intentional I don't think.

[narmadhahearty]

fourth dimension is time and one cannot jump out of it.but nothing is impossible.but the concept of time travel though worm hole exits,if you dare to travel through time you will only create multiple copies of yourself.because energy can neither be created nor be destroyed.

[Stuugie]

fourth dimension is time and one cannot jump out of it
but the concept of time travel though worm hole exits

If you go back in time, and I mean make the concious decision to do or not do it, you will in fact be jumping out of your natural time-line. Making copies of yourself seems an interesting point of view. Also, energy can be created, with energy of course.

[janeleonard]

4th dimension is something that needs to be explained more in detail as it is related to time and seems to be complex.

[Hiroshe]

A 4th dimention is not neccasarily related to anything in particular (including time). It's simply another index for whatever your dealing with. Trying to extend geometry to 4 dimentions is what doesn't make sense (though, it is possible when we make generalizations). It's not complex at all. Arbitrary and infinit numbers of dimentions are natural in linear algebra and calculus.

[rkwickstrom]

As I understand it, quantum mechanics would accommodate 10 spacial dimensions. Only 4 dimensions of space-time unfolded, so this question could be a great deal harder to answer than any of us realize...

[Stuugie]

It occured to me that since time is not constant but rather relative to the observer, could it really be a part of dimensional thinking?

[ddanbe]

When you're flying in an aeroplane you could say you travel in six dimensions. {x, y, z, pitch, roll, yaw} Read this article.

[Hiroshe]

It occured to me that since time is not constant but rather relative to the observer, could it really be a part of dimensional thinking?

If you wanted to, you could use time as some index if it's releavent to the problem at hand. There no reason why you couldn't use it (it is used as an index in practice a lot), and there's no reason why you should if it's not relevant to the problem at hand (again, often in practice we look at instances of time, or if we're dealing with things with arbitrary numbers of dimentions unapplied to the universe).

We've observed that the faster an object goes, the faster it precieves time. What interesting here is that there are a lot of different ways we can correctly state this as long as it's mathematically equvalent. So, another equvalent we can say us that: "the faster something goes, the slower the interactions between it's elementary particals happen (since all interractions can be modeled on that level)." So it's a little more like it's slowing down rather then traveling through time (though you are preceiving time as going faster as the observer; in the same sense that you'd "jump" through time if you were frozen in ice and somehow revived.)

[heidi.dum]

Using time to represent the 4th dimension doesn't gain us really anything because we cannot change time. As mHeath said above- if you start 2 hours behind, you will always be 2 hours behind.

Light can be a good example of the 4th dimension as it can be added or taken away. The affect of light we see everyday, young children understand the 4th dimension wrt light in reality. A persons shadow is created by the 4th dimension element of light. As the light moves so does our shadow. If the light is removed completely, exactly noon, or pitch black, we also have no shadow.

Another way to think about it is if you take any two dimensional polygon with more 4 verticies- 4 are needed to create a pyrmarid- and connect each one with every other one possible. The simplified explanation is the fact that you now have internal and external faces has created a 4 dimensional figure. It is easy to see when you rotate the figure.
This video does a good job demonstrating that. The first few minutes show that, the rest imo is just more examnples.
https://www.youtube.com/watch?v=rG6aIVGquOg

[Hiroshe]

Using time to represent the 4th dimension doesn't gain us really anything because we cannot change time.

We can still use it as an index. For example, we can talk about events that happened in 1964 because we are using time as an index to specify 1964.

Another example would be a movie. Or a computer simulation. In these cases, we're not talking about using the universes time, but we are still using the measurement of time to index through something.

Light can be a good example of the 4th dimension as it can be added or taken away. The affect of light we see everyday, young children understand the 4th dimension wrt light in reality. A persons shadow is created by the 4th dimension element of light. As the light moves so does our shadow. If the light is removed completely, exactly noon, or pitch black, we also have no shadow.

That's very vague, where as dimentions is a mathematically concrete idea. How are you using light as an index for anything? It's not impossible if you set up a(n) equation(s) representing a feild, where luminesce is a variable (thus giving you a set of feilds indexable by light); but that doesn't corrilate to your real world situation. A person's shadow is created by very normal 3 dimentional geometry.

The simplified explanation is the fact that you now have internal and external faces has created a 4 dimensional figure. It is easy to see when you rotate the figure. This video does a good job demonstrating that. The first few minutes show that, the rest imo is just more examnples.

4-dimentions simply does not make sense geometrically. We can make generalizations. We can also make 2 or 3 dimentional projections of what a 4 dimentional object. This demonstrates the idea of how much information is required to construct a 4-dimentional shape; but it's important to note that the 4d figure itself is simply nonsense.

[Reverend Jim]

Do you recall a Kodak commercial from years ago with Mariette Hartley and James Garner. He says to her, "that doesn't make sense." She replies, "you mean you don't understand it."

[Hiroshe]

Do you recall a Kodak commercial from years ago with Mariette Hartley and James Garner. He says to her, "that doesn't make sense." She replies, "you mean you don't understand it."

If you can find somewhere that makes sense of the existance of a physical 4-dimentional object, I'll certianly be glad take a look! But I'm not basing my comment on "I don't understand it, therefor it doesn't make sense for anyone." Rather, I'm basing it on my own exploration into the feild (mostly from the geometric applications of linear algebra) as well as comments from an undenaibly good professor.

We've (the class) talked about this with my Calculus professor who proclaims himself a geometer, and he's mentioned that it's simply not possible to make sense of a physical 4-dimentional object; it doesn't have a physical interpretation. Obviously it can be projected just like any other vector space; thus we can "see" projections of it in 2D or 3D.

It's not a matter of not understanding it. It kind of remind's me of this video. It's not that the expert doesn't understand geometry and thus cannot draw 7 perpendicular lines - it's that he does understand geometry and it's impossible to draw 7 perpendicular lines.

[almostbob]

time as a fourth dimension is simple to understand
a floor plan is a section across the z dimension, and the time dimension
an elevation is a section across the x dimension, and the time dimension
or elevation is a section across the y dimension, and the time dimension
your baby photo, teenage photo, wedding photo, retirement photo, are sections across the time dimension, and the x y z dimensions
the time dimension is enormously important.
It is simple to stand on the train tracks in front of a train, as long as the train's position on the time dimension is 'yesterday'
it just is bloody difficult to produce a linear drawing along the time dimension.

[almostbob]

This u tube is a linear along the time dimension, 12 years long,

[heidi.dum]

Your Calculus professor claims himself to be a geometer? As in an expert in geometry?
As him about the difference between Eculidean and non-Eculidean or hyperbolic Geometry.
If you look at the connection of non-Eculidean geometry and 4th dimension art, it may help you gain an understanding if you are still confused.

[Hiroshe]

Hyperbolic Geometry (an instance of non-Euclidean geometry) can be generalized to n dimentions if you wish (just like Euclidean geometry). The only difference between Euclidean Geometry and non-Euclidean geometry is the fifth-axiom. However, you still face the exact same problem: there is no interpretation of a 4-dimentional object. Hyperbolic Geometry make no attempt as far as I know to come up with some interpretation. In fact, I don't see why it would make an attempt to do so - Hyperbolic geometry isn't based around multiple dimentions (though as I said, just like Euclidean geometry it can be generalized), it's based around changing the 5th axiom.

It's kind of like changing the colour of a pen, and expecting it to change the answer.

Your Calculus professor claims himself to be a geometer? As in an expert in geometry?

I guess so. I think it also means that he tries to think of the problem geometrically, and works off of that to work out a solution. I've seen him remember theorums by using geometric hints for example.

[Hiroshe]

An easier way to understand this:

We can visualise an r->r function onto a 2D plot because what we know what "our" 2D is (it's a surface in our world). We can visualise an r2->r function onto a 3D plot, becasue we know what "our" 3D is (it's just like an object in our own world). We cannot visualise an r3->r function onto a 4D plot, because we have no idea what 4D is (we have no "our" 4D in terms of geometry of this world). For example, the idea of Perpendicularity needs to be generalised to Orthogonality before we can use it in higher dimentions (because perpendicularity is based on our world). This is generally defined by an inner product which can be chosen to the feild we're working with. Furthermore, even if we did make a generalized 4D world that in theory could be visualised by some being; our brains simply don't have the capabilities of creating a visualization of it.

That's not to say we can't work with functions in r3->r; it's just that we don't have a physical interpretation for it (and attempts to do so, which some people try to do, are senseless). We can of course do things like project it into 3D or 2D. That's just a bit of simple linear algebra.

We can also of course specify the "dimentions" of r3->r to be different things (like for example 3 geometric coordinates and the function returns the tempurature. Or for r4->r it can be 3 geometric coordinates and time and returns electric charge, which is now 5 points of information.)

[heidi.dum]

As almostbob stated earlier one of the easist to comprend examples of the 4th dimension is time when looked at past and present opposed to just the present. In the present two things always have the same relationship, thus the 4th dimension time does not apply. However, time as a 4th dimension element as in over time is an easily grasped idea, photos provide a wonderful tangable example.
The idea of light as a 4th dimesion element I mention earlier and how it casts a shadow on a 3 dimensional object also is an example that is easy to grasp.

When people think of non-Eculidean geometry most often they think of hyperbolic or elleptic. The 4th dimension does come into play especially in elleptic. When you get into design such as archeticuture and especially landscaping and shadows become important as they have a major impact on plant growth. When we teach non-Eculidean geometrey the first thing we usually do is have students start with a 3 dimensional graph of a sphere and super impose a 2 dimensional graph over that and graph the shadow of the sphere on the 2D graph, or simply on the x,y plane of the 3D graph.

Non-Eculidean geometry allows us to work with curved objects much easier, and allow us to understand how lattitude and longitude lines are parrallel, yet not parrallel.

[Hiroshe]

As almostbob stated earlier one of the easist to comprend examples of the 4th dimension is time when looked at past and present opposed to just the present.

Correct. 3+n dimentions can make sense when the other n dimentions are not geometric. Inclusing time, colour, static charge, magnetic feild strength, current, density, practically any observable property. The problem becomes fairly easy and clear to grasp in those situations.

The idea of light as a 4th dimesion element I mention earlier and how it casts a shadow on a 3 dimensional object also is an example that is easy to grasp.

I don't understand this point. We can and do project shadows using 3 dimentions. I can fire dust from a "dust cannon" at someone for example, and see an imprint of them on the wall behind them. Each of the particles has a very simple trajectory (not including graviety or air resistance). It's easy to tell which particles hit the wall, and which don't by checking for intercepting with the trajectory and the object. This boundry can be calculated continuously as well. The process is well defined, and a 4th dimention doesn't appear anywhere in the process (and even if the calculation did involve a 4th dimention, does it actually involve a physical interpretation of a 4 dimentional object in geometrical space itself?).

The 4th dimension does come into play especially in elleptic.

Don't get me wrong, I'm not saying that dimentions above 3 don't make sense. Anyone who's explored linear algebra and calculus has worked from 2 dimentions to an infinite number of dimentions. I'm saying that a physical geometric interpretation of a 4-dimentional object is nonsence. I'm also not saying that more then 3 dimentions don't play a part in geometry.

[heidi.dum]

The light and the resulting shadow is the 4th dimential element, resulting from an action on a 3 dimensional object.
Same concept as your dust cannon. It is another dimention or plane in relation to the person that the dust cannon is fired at.

[mattster]

When we grew up, I was really good friends with a lad called Chris. Chris was always a gifted mathematician, and at 17 went to Cambridge to study maths.

He carried on to do his PhD, studying the concept of a 4th dimension, of which he was awarded a fellowship and remains in charge of a research team there.

I'll have to ask him what he thinks about all of this aha ;)

[Hiroshe]

The light and the resulting shadow is the 4th dimential element

Both the light and the shadow (the lack of reflected light) geometrically exist within 3 dimentions.

Nothing about dust (geometrically) is 4 dimentional.

3D Objects are allowed to hit other 3D objects without ever requiring a 4th dimention.

He carried on to do his PhD, studying the concept of a 4th dimension, of which he was awarded a fellowship and remains in charge of a research team there.

Nice. Does he have any papers published?

[mattster]

He might do, I wouldn't know where he'd put them ;) I'll ask aha