The 5th Dimension

[cwes99_03]

The reason is that gravity is a radial force not a euclidean. Macro measurements of gravity always measure the effects towards the center of mass radially outward.

 

I have done physical experiments in 4-d. Once one figures out that orthogonal in electronics just means that everything has to be conceptually orthogonal. Twist your mind around what a 4-d hypercubic lattice looks like and then start soddering.

[ughaibu]

Cwes99_03: Thanks. Yes, I'd been considering Euclidean space as defined relative to the individual and thus with the vertical radial to the Earth's centre, but such a system would play havoc with the parallel postulate and compromise Euclid's idealism, so, pretty much nonsense, I guess.

I like the circuitry aspect. While casting around for ways of conceptualising spaces of more than three dimensions, I tried looking at the number of spaces of particular dimensions, within particular dimensional spaces. For example, I considered a 2-dimensional space of (area) one, to have two 1-dimensional elements of (length) one, a 3-dimension space to have three 1-dimensional elements and three 2-dimensional elements, as there are three combinations by which two dimensions can be constructed from a total of three dimensions, a 6-dimensional space to have fifteen elements of 4-dimensional space, etc. While jotting down the figures it occured to me that if I added a 0-dimensional element with a constant value of one in spaces of any dimension, the figures would describe Pascal's triangle. Changing the base value from one to two, gives an untriangular set of figures, that might be more interesting. I haven't decided yet, if or how the idea is worth more thought.

[cwes99_03]

That last comment was very thoughtful. It took me two 3 hour days to figure that out when I started my experiement. A professor started me on the path because he knew it should be able to be done, but I had trouble visualizing more than 3 dimensions. I understood time as a 4th dimension only because i could picture a group of concentric spheres (like the earth) moving through time. As the spheres move from t=1 to t=2 the 3-d sphere just moves along an axis. Most people understand this.

Now try building a 1x1x1x1 hypercubic lattice. The key to doing this is to start building the same way you would a 2-d or 3-d lattice, that is one dimension at a time.

 

You take a line. Add another line at 90 degrees, you have 2-d. Add a third line at 90 to the 2-d plane and you have 3-d. In a flat drawing you can do this by simply drawing two overlapping squares and connecting the proper corners. This is the break-through thought. How do you now add a third line 90 degrees to the cube? Well to draw it you simply draw two cubes and then connect the proper vertices you will have drawn a 4-d hypercubic lattice.

Now visually, your mind has a lot of troubles with it because it appears that some of the planes are bisecting each other. Physically If I were to grab 2 cubes and try to connect the proper sides with panels of wood, it would be physically impossible, because we live in a 3-d world, (unless you understand string theory, which I still haven't tackled.)

However, to me this was unimportant. All I had to do was figure out how to wire up something in higher dimensions cognitively. While some will argue that all I really did was create a super complex 3-d shape (that is not a hypercubic lattice but some other shape) the conceptual understanding of the layout of the resistors was 4-d, namely that vertice 1,1,1,0 was connected to 1,1,1,1 to form a side.

While I said earlier that I soddered them up in that fashion, my real triumph was designing a system to create it all on a soderless breadboard (2-d surface). That took a couple of hours and my physics professor got excited when he saw what I had accomplished. I believe I'm still the only person to have ever wired something up in 4-d and 5-d. I had some pictures somewhere of my designs, and my lab notes and results from my first couple of runs are all still housed at Illinois Wesleyan in the physics department.

[UncleAl]

You can mathematically erect as many orthogonal spatial dimensions as you like. In physical theory you can go Kaluza-Klein. You can play with the various geometric dimensions of string theories or waffle with "one charge dimension, two isospin dimensions, and three color dimensions" added to three spatial and one time to get 10 dimensions

 

Even organikers are in on it. Legendre polynomials are orthogonal and they certainly aren't straight lines.

[CHADS]

If the point of so many dimensions is flexibility how many would the universe need .... so many dimensions seems like the universe has evolved complications along the way .... maybe the universe has created the dimensions in its evolution or the dimensions where there for it to fill ... What ye think?:hyper:

[ughaibu]

Cwes99_03: I guess your model is similar to Qfwfq's (post 13 at http://hypography.com/forums/philosophy-science/6395-understanding-3-spatial-dmensions-2.html?highlight=gardner). Here are some more ideas: http://en.wikipedia.org/wiki/List_of_regular_polytopes

[cwes99_03]

Yes, you can find those on the internet as well when looking for 4-d hypercubic lattices. But just staring at them doesn't always lend how to visualize them, as I mentioned earlier. But using Q's pic, one can use the description I gave and visualize how to create that drawing over.

[Farsight]

Like this?

 

http://mrl.nyu.edu/~perlin/demox/Hyper.html

 

ANybody know a good one? There was one I looked at years back and wow, I saw it. It's kind of like those colourful picture puzzles that were all the rage in newspapers a couple of years back. You squint at them for a while moving your head back and forth, then it clicks, and suddenly there's a 3D image with about an inch of depth in the thickness of the newspaper.

 

And I do so like those Escher paintings.

[cwes99_03]

Thanks, yes, like that. But this isn't about hidden images, this is about higher dimensions and how to find them if they exist.

[Farsight]

I read something about Flatlanders, perhaps it was one of Michio Kaku's books:

 

A two dimensional Flatlander whose existence is limited to a surface (eg a piece of paper) would have no concept of any rumples in that surface. If he was climbing one of the rumples, he wouldn't know he was climbing into the third dimension. But he would feel a force that meant he had to work harder to traverse that region. The point was, that all the mysterious "action at a distance" forces such as gravity and magnetism can be considered as distortions in one or other dimension that we cannot perceive directly.

[ughaibu]

This page looks interesting: http://members.aol.com/Polycell/glossary.html#H

[Farsight]

Here's something else of interest, a newpaper article:

 

http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2005/06/01/ecfdime01.xml&sSheet=/connected/2005/06/01/ixconnrite.html

 

Lisa Randall, one of the world's most influential physicists, explains why we need more than three dimensions to understand the cosmos

 

Scientific progress always entails an almost contradictory set of beliefs. You need to make assumptions to build a mathematical picture of reality. But while you want to be sufficiently excited about your assumptions to think they merit investigation, you need to remain sceptical enough to subject the consequences of those premises to rigorous analysis.

 

Although I've always combined these attitudes in my research, my recent studies of extra dimensions of space, beyond the familiar "up-down", "left-right" and "forward-backward", have made me more than usually convinced that they must really exist.

 

Perhaps the best way to understand what these extra dimensions would be is the way Edwin Abbott described them in his book Flatland, written in the late 19th century. Suppose there was a society that, unlike ours, could detect and experience a world with only two dimensions: the Flatland of the title. Its inhabitants wouldn't perceive a third dimension, even though the dimension really did exist..."

[arkain101]

Lisa Randall, one of the world's most influential physicists, explains why we need more than three dimensions to understand the cosmos.

 

 

I dont think I fully agree, but who am I to argue.

I think we ALSO need to step back and look at some crucial basics. Then step forward again slowly using the new found logic in those basics and the prior knowledge and work on combining for theory.

 

For example, the version of time I present, the pair relationship principle, and the super-nature plausability.

(these are not official titles. Though, they suffice)

[ughaibu]

There's a claim in that article that physicists and astronomers "discovered" dark matter, is that so? I thought dark matter was a conjecture to fix the maths.

[Farsight]

I believe it's a "postulate", ug. Here's a quote I found:

 

"Dark matter explains several anomalous astronomical observations, such as anomalies in the rotational speed of galaxies (the galaxy rotation problem). Estimates of the amount of matter present in galaxies, based on gravitational effects, consistently suggest that there is far more matter than is directly observable...

 

There are other theories, such as gravity having a component that makes it "non-Newtonian" on a very large scale, wherein it doesn't follow the inverse square rule.

[ughaibu]

Thanks.

[Glenn Lyvers]

This is one big doubt i have got from a long time. :)

 

The four dimensions i can see and visualize are

 

( x, y, z) and ofcourse time (t) forming the space-time

 

Is there a fifth dimension too?

If so, what is it?

Can we experience it in our day to day life?

:(

 

There is only speculation that time is a dimension at all. And if is it, does time incrementally unfold like a spiral into our universe, or is it we who are actually passing through the dimension of time, which already exists in the past, present and future.

 

If time is a dimension, there is no evidence that it would be the 4th. It might be that the 4th is spacial, and the 5th it time. Or it could be that spacial dimensions are infinite, therefore time would not be the same type of dimension, it might be some type of universal which cuts through all spacial dimensions.

 

(from wiki)

In mathematics, the dimension of Euclidean n-space E n is n. When trying to generalize to other types of spaces, one is faced with the question “what makes E n n-dimensional?" One answer is that in order to cover a fixed ball in E n by small balls of radius ε, one needs on the order of ε−n such small balls. This observation leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension. But there are also other answers to that question. For example, one may observe that the boundary of a ball in E n looks localy like E n − 1 and this leads to the notion of the inductive dimension. While these notions agree on E n, they turn out to be different when one looks at more general spaces.

 

A tesseract is an example of a four-dimensional object. Whereas outside of mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions," mathematicians usually express this as: "The tesseract has dimension 4," or: "The dimension of the tesseract is 4."

 

... Considering time as a dimension is common, but don't get hung up on the idea that it is necessarily the 4th, or 100th.

 

I hope that helps get the brain whirling around more.