I KAN HAS 4D?

Just been watching these videos on 'thinking in 4 dimensions'. Thought you guys might enjoy it. What can I say, I like the pop-up-book versions of 'Mind altering' subjects.

 

http://www.dimensions-math.org/Dim_regarder_E.htm

Oh wow. That was actually pretty insane.

first off let me say... that not only is the full of BS

 

 

 

but lets look at the basics of the principle for the "4th dimension"

 

def: A physical property, such as mass, length, time, or a combination thereof, regarded as a fundamental measure or as one of a set of fundamental measures of a physical quantity

 

 

the video did show that this existed but..................................

 

the video requires that the earth be a perfect sphere... (hate to break it to you but its not) soooooooooooo everything said... is a lie

 

 

 

 

the only way i see possiblity of another dimension

 

now the possiblity of a 4th dimension in its in essence would have to exist on a much grander scale lets look at the scope of the universe.

 

now seeing how light speed is a unit for time and not distance techinically we would be looking into the past. so galaxies forming must be in essence in the far reaches of space formed the roughly about the same time as our galaxy.

 

and lets say that our universe in a sense is a big rubber sheet you cannot get off of the rubber sheet because you are the rubber sheet. now the only hopes of essentually of a 4th demention would be proven though the exploration of black holes because it would be like putting a pin through the rubber sheet and stretching it EXTREMELY far up and down and just like rubber our universe would have to have a breaking point... (so if you where in a sense able to surivive going through a black whole) you would enter a completely diffrent plane or rubber sheet. (another demention)

 

you cannot fly across a black whole because you are embedded in the rubber sheet.

 

also for other demessions to exisit string theory would have to be proven...

 

the reason string theory has not yet been for sure is due to approximations necessary to work with particles at low energies in small spaces. The approximations physicists make at these levels are based on previous data which relyed on or derived from observation or experiments. This means that the theory itself seems to make no new predictions.

 

However, this is not entirely true. There are currently some physicists who believe that string theory is actually testable using current technologies. Also, it is almost certain that the Large hardon collider at CERN will be able to test some predictions made by string theory. It is probably just a matter of time now before we can start to empirically verify/falsify String Theory.

 

 

 

 

 

 

 

 

... i learned something me thinks in school

Edited August 25, 2008 by Bangudray

Bang, go back to being a whipping boy.

This large hardon collider.... does it have anything to do with Hard Gay-san?

because it should

FUUUUUUUUUUUUUUUU~

I'm convinced that those videos would make more sense if I was stoned.

 

And Bang, when the hell did you bone up on Cosmology and Physics?

well ecth ill tell you a story

 

pat cant make up his mind on a major, i think another word for it would be ADD

 

and you guys never talk to me about these sorts of things lol

 

subjects i know a lot about

-psychology (3 classes in it)

-History (damn history channel) (4 classes in it)

-biology (3 classes in it)

-universe (astrology) (2 classes in it)

-general sciences (not super detailed but ok) (in total about all together including mentioned above about 18 classes)

 

-recently geared into engineering so learning more on this (3 classes around in this area)

 

 

 

math i hate... uber bad

as you can tell english is not a strong subject

nor is any forgein language maybe due to reason above lol

 

 

++++another long post btyb bang+++++

 

meh, idk, maybe it's just me but i found that all a creative thinking of, i guess you could say, pinpoint perspective and nothing to do with a dimension. geometry. maybe i just don't really understand it, but even if i did i just wouldn't find the significance of that.

 

from my understanding in the first place the fourth dimension would be time, which.. i'm pretty sure you incorporated Bang

 

either way that video was interesting as hell o.O

Edited August 25, 2008 by Letica

It was pretty interesting, but Bang did make a valid point. Everything was based on the fact that the Earth was a perfect sphere... which it isn't.

So...I take it no one actually watched the whole thing. This video has little or nothing to do with astronomy or cosmology in its presentation. As a disclaimer, the authors of this video never say the Earth is a perfect sphere; in fact, in Chapter 1 they acknowledge that the Earth is flatter at the poles (Chapter 1, 1:48-1:51), but only want to draw your attention to a perfect sphere shape so that they can explain some geographic and geometric techniques. Furthermore, outside of Chapter 1, the video never says the word "Earth" again, and in no way attempts to make Physical (as in the science of Physics, not something you can touch physical) interpretations of what a 4th dimension would mean in terms of space-time, so for the people above me who are saying "it's all based on a false assumption", I am right in assuming you didn't watch all 10 chapters of the video. I have my own commentary on this video at the end, but here's an outline to dispel this whole "lawl this is all false" nonsense.

 

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Chapter 1

Geography - The study of mapping the Earth

Geometry - The study of measuring the Earth

Introduces the ideas of parallels (biggest parallel is the equator) and meridians (most significant is the prime meridian, through Greenwich, England.)

 

This whole chapter is devoted to explaining the idea behind stereographic projections. A stereographic projection takes all the information from the surface of a 3 dimensional object and maps it down to a 2 dimensional space. Starting from the highest point on a sphere (north pole for the Earth example), lines are drawn through the north pole, THROUGH the inside of the sphere, and reappear at another point on the surface of the sphere. These lines are then extended onto a plane which is perpendicular to the south pole (i.e., if you set a ball on a table, then the table is the perpendicular plane to the south pole), and all of the information is drawn out onto the table. The projection (table) image preserves all shapes, but doesn't preserve the measures (preserves a figure's geography, not its geometry). Such projections are called "conformal".

 

Chapter 2

This chapter deals with showing us how 3 dimensional objects are perceived from a 2 dimensional perspective. That is, how would you explain what a 3 dimensional solid (polyhedron) is to someone who only sees the world in 2 dimensional solids (polygons). The video gives two methods:

 

1) By passing a polyhedron through a plane, you observe all of its cross-sections. These cross-sections can vary based on the angle at which you pass the polyhedron through the plane (for example, if you stand a cube flat on a square face, you always see a square cross-section from a 2D perspective; however, if you stand a cube on its edge, you see a line, then a rectangle, a square as the middle passes through the plane, back to a rectangle, and then a line before it disappears again). As the narrator points out, this method is particularly difficult to understand, because it requires a lot of intuition about all the possible cross-sections of a polyhedron.

 

2) Inscribe a polyhedron into a sphere, so that all the vertices of the polyhedron touch the surface of the sphere. Then, round out the edges of the polyhedron until they too touch the surface of the sphere. Color each face of this "inflated" polyhedron differently, and stereographically project this new sphere (divided into faces) onto a plane. As pointed out in Chapter 1, this method will preserve the geography of the polyhedron, not its geometry. So in this method, counting the number of different colors on the plane will allow you to know the number of faces of the polyhedron you began with. This is much easier than method 1, as all of the information of a 3 dimensional object is translated in one unique way into 2 dimensions, whereas the former method had many non-unique ways of taking 3D info to 2 dimensions.

 

This section is presented to us because we can understand readily both 2 and 3 dimensions. The narrator then hopes to give you some kind of understanding of what a 4th dimension would be like (geographically and geometrically) by taking the same analogy of stereographic projections from higher dimensions into lower dimensions.

 

Chapter 3

This section deals with the 4 dimensional analogue of the "cross-section" method outlined in Chapter 2. When we passed a 3 dimensional polyhedron though a plane, we could observe 2 dimensional cross-sections, which varied based on the angle at which the polyhedron was moved (remember the different sections of a square if you started flat or on an edge). The narrator then continues this analogy into 4 dimensions. If you could (hypothetically) pass a 4 dimensional object through our 3 dimensional space, we would observe changing 3 dimensional cross-sections of this 4D object. So, by this reasoning, there exist 4 dimensional objects whose 3 dimensional cross-sections are tetrahedrons, cubes, dodecahedrons, icosahedrons, etc. As with the analogy in 2 dimensions, this method doesn't give a good feel for what the higher dimensional object looks like, as the cross-sections can and do vary based on how they pass through the lower dimensional space.

 

Chapter 4

This section deals with the 4 dimensional analogue of the stereographic projection method. Just as before when we "inflated" a 3 dimensional object in a sphere, then projected that sphere onto a plane and observed the results, the narrator (with some help of your imagination) places a 4 dimensional object (which you cannot see) into a hypersphere, and stereographically projects it down onto 3 dimensional space. The results are really intricate, conformal 3D objects, all with great symmetry, and are really well rendered by this video. Again, this section does not claim to show you a 4 dimensional object, because we have no way of viewing it because our senses are bound in 3 dimensions; however, they try to give you an idea of how 4D objects interact in 3 space by showing you these stereographic projections, much as the 3D objects interacted with the plane in 2 space. Really worth watching this section for the animations.

 

Chapter 5

A really great introduction to complex numbers. Not much to say, the section is really self-explanatory and well done. One thing worth noting is that now points in a plane can be described with one complex number (as explained in the video), whereas before we needed 2 real numbers to describe a point in the plane. That is, with complex numbers, a plane is dimension 1, instead of dimension 2. By extension, the end of this chapter shows that the stereographic projection of a sphere into the complex plane (1D) is a 2 dimensional line (remember before the projection of the Earth (3D with real numbers) was a 2D plane). Hinting that now we can describe 4 dimensional, real number valued objects in 2 dimensional complex space.

 

Chapter 6

A look at complex transformations, Julia sets of complex transformations, and the Mandlebrot set (a set of complex numbers for which the Julia set exists), and the resultant fractal sets they produce. Really beautiful stuff, but this section does not go into great detail about fractals (which is a pity, since a lot of image storing software today utilizes fractal decomposition to store pictures without quality loss). Worth watching for the pictures, but probably beyond the scope of non-math people.

 

Chapter 7

An extenuation of the idea of mapping 4 dimensional real valued objects into 2 dimensional complex space. Deals with Hopf Fibrations, which are these really neat objects made up of infinite amounts of interlocked, non-intersecting rings (which is really a 2 complex dimensionsal simplification of a 4 real dimensional hyper-sphere). This is Topology 101, and the pictures are really wonderful, with good explanations. Not for the Math faint-of-heart.

 

Chapter 8

A further look at Hopf fibrations, as well as Villarceau circles on a torus. Simply put, a torus is a shape you would get if you took a circle, and rotated it around a line (think dount shape). On a torus, there are four families of Villarceau circles (explained in detail in the video as bitangential, parallel, and meridian). When these circles are seen together, they produce a Hopf fibration. What's interesting is that we have found with Villarceau circles a 2 real dimensional way to describe a 2 complex dimensional object (Hopf fibration). But by extension from Chapter 5, this means we have some more insight into the world of 4 dimensions, since a 2 dimensional complex space is analogous to a 4 dimensional real space. It's all pretty uphill from here, and most people don't cover this level of topology until graduate school.

 

Chapter 9

A pretty well thought out proof explaining why stereographic images work. Nothing to explain, as the video outlines the proof in detail using geometric theorems in both 2 and 3 dimensions (real dimensions), and makes the analogue to 1 and 2 complex dimensions. Easier to understand than Chapters 7 or 8, but still requires a good background in math to appreciate.

------------------------------------------------------------------------------------------------------------

 

I really wanted to outline this video because it is EXTREMELY well done. Chapters 1-3 are pretty accessible to anyone despite your background in Math. Chapters 4-6 are good for those with some college level Math background, while 7-9 are really for senior level undergrad/grad students. I got a little upset when someone earlier in this thread said everything in this video is a lie...because it's just simply not the case, but I'm sure hardly anyone has watched the whole 2+ hours of this anyways.

 

I've already watched it 3 times through, and its wonderfully done, and they are releasing a "Dimensions II", which will cover more Topology and Dynamics. Math rox!

Edited August 25, 2008 by Ryee

Thanks for summing it up, Ryee. The point of the whole thing was conceptual. When we know everything about a subject it ceases to be a science...As in 'the study of'.

I'll admit I watched the first little bit of the film, saw the globe being cut up and had a flashback to Geography from grade school. I then moved on. <3

this thread has lots of words

this thread has lots of words

srsly

 

http://img.photobucket.com/albums/v145/cheap_shot/funny%20crap/646deon.jpg

oh o.O

 

crap, i didn't see all the other chapters ryee.

 

thanks :]

 

EDIT:

mah mind.. is blown.

o.O

 

thankfully i'm starting geometry this year, so a good amount of the things i picked up in that will help out a lot.

 

/smart

Edited August 26, 2008 by Letica

i just saw that special last week on the giant particle accelerator. I find all this speculation so interesting. If we didn't have scientists pushing the envelope every day (and people calling them crazy) we wouldn't have a fraction of the technological advances that we have to this day.. thanks for posting this. i'll try and check out that video when i have some time.

 

Also no direct offense to you bang, but I have a pet peeve about people who claim to know a lot about a certain subject because they have taken a few college level classes. I have two Bachelors degrees from Villanova University Psychology and Sociology class of 2001 (hooray fireworks pl0x) and even in those areas i still have so much to learn (master's/Doctorate?), let alone getting a minor in a sunbject, a concentration in a subject or even so little as a few classes. My school required us to have a well rounded education so i have a good 2-3 classes in all the major subjects as well as some not so major. I know a guy whos shelf is lined with all these "_____ for Dummies" books. which they make for everything and anything.. he reads it and then hes the expert. Again im not saying that's you bang, but im just saying lol... (stepping off my soap box)

 

anyhow.. very cool post and thanks for the outline.. well written i might add

One could argue, time is the 4th dimension. But then again someone else could argue...

 

EDIT: LOL Atrus, I love that pics. "Life, sometimes even the sprinkler wants you dead."

Edited September 22, 2008 by Joesf

One could argue, time is the 4th dimension. But then again someone else could argue...

 

EDIT: LOL Atrus, I love that pics. "Life, sometimes even the sprinkler wants you dead."

Actually, I was gonna mention that. 'Bodies in motion', etc...Anyway, as I stated before, correct or incorrect (Come on Bang! This is theoretical, not pop quiz 2008!), I enjoy this kind of pontification.

First of all: Ryee, your time is pretty pissed off with you, seeing as you wasted about 3 hours of it writing a post that no one was gonna read. GG.

 

And also: Bang, when you learn the difference between frostbolt and fireball I'll listen to what you have to say about theoretical cosmological physics.

I read your post ryee XD I just didn't watch the video yet

First of all: Ryee, your time is pretty pissed off with you, seeing as you wasted about 3 hours of it writing a post that no one was gonna read. GG.

 

And also: Bang, when you learn the difference between frostbolt and fireball I'll listen to what you have to say about theoretical cosmological physics.

 

Troll harder? I didn't write it in the hopes that the local stoner would walk away with a new view on life.

 

:eyeroll:

Eye roll thiiiiiiiiis

Oh nO He Di INT

Oh nO He Di INT

O yA He Di ID

youre gonna make bang cry, RH