4-D shapes

[Mikeus Caesar]

http://fourd.ytmnd.com/

I tried imagining holding one in my hand and my brain melted.

Seriously - what the hell!?

[doc_bean]

4D objects projected on a 2D plane ? Bound to get weird...

[Mikeus Caesar]

http://universe3d.ytmnd.com/

4D objects had one weakness...

[UltraWar]

I've seen the 4D shape one before! :laugh4:

[JimBob]

What is the first dimension? A single line going to infinity in both directions, how do you split it in half? A single point.

What is the second dimension? A plane streaching to infinity in all directions. How do you split it in half? A single line (1D object).

What is the third dimension? A cube streaching to infinity in all directions.
How do you split it in half? A plane (2D object).

So what is the fourth dimension? Something that could be split in half by an infinitley large three dimensional object.

[Glaucus]

If you think about out, there is nothing 1D in the world... everything has at least 2 dimensions if you keep magnifying it.

[ajaxfetish]

Well, theoretically point masses should exist in fewer than 2 dimensions. But they're not really observable at present, if they exist.

Ajax

[Beirut]

Anybody here ever read Flatland?

Brilliant little book!

[Divinus Arma]

4-d shapes. I was expecting something completely different. :laugh4:

[Ironside]

http://fourd.ytmnd.com/

I tried imagining holding one in my hand and my brain melted.

Seriously - what the hell!?

Actually there's no problem holding that object. It will simply look like a cube. Where it get's weird is if the object moves through the fourth dimension, as it will suddenly disappear when the cube no longer has a volume in our 3-dimentional space.
A ball is even weirder as it will look llike a regular ball that'll continue to grow/shrink as it passes through our space.

Atleast that's my understanding comparing 2-D with 3-D and applying the changes into 4-D.

[The_Mark]

http://www.kleinbottle.com/
Get yours today.

[The_Doctor]

The 4th dimension is time.

That object at the end only had 3 spatial dimensions.

[ajaxfetish]

At first, I thought 'what a sham, they just stretched a cube to make it seem to go into a new dimension, it's still actually just 3-d.' Then I realized, 'no it's actually still just 2 dimensional, as the third is an optical illusion, or perhaps symbolism of depth.' In that sense, stretching the cube of course doesn't make it an actual 4 dimensional object, but with the 4th dimension being time it makes as much sense to let that final stretching represent motion in time as it does to to let the previous one represent motion into a 3-dimensional space.

Hmm, hope that made sense.

Ajax

edit: In fact, imagining holding a 4-d object in your hand shouldn't be a problem, as technically everything you've ever held in your hand has been 4-dimensional (or more if you're into string theory, but I'm not going there). A pencil not only has 3 spatial dimensions, but exists as time changes as well.

[The_Doctor]

At first, I thought 'what a sham, they just stretched a cube to make it seem to go into a new dimension, it's still actually just 3-d.' Then I realized, 'no it's actually still just 2 dimensional, as the third is an optical illusion, or perhaps symbolism of depth.' In that sense, stretching the cube of course doesn't make it an actual 4 dimensional object, but with the 4th dimension being time it makes as much sense to let that final stretching represent motion in time as it does to to let the previous one represent motion into a 3-dimensional space.

I understand what your saying.

If you think about it, its on a monitor, so it only has length and hight plus time, so it is only has 3 dimensions.


or more if you're into string theory, but I'm not going there

That would be fun, until it kills half of the Org.

[Kanaric]

I remember watching something that said the 4th dimention is time, lol. Probably some bad sci-fi though and not anything real.

[Moros]

Actually there's no problem holding that object. It will simply look like a cube. Where it get's weird is if the object moves through the fourth dimension, as it will suddenly disappear when the cube no longer has a volume in our 3-dimentional space.
A ball is even weirder as it will look llike a regular ball that'll continue to grow/shrink as it passes through our space.

Atleast that's my understanding comparing 2-D with 3-D and applying the changes into 4-D.
That's if you'd put a 3D object in a 2D world 4D is different. I've found animations about this a long long time ago (I think a year or two) in which showed the 4D equivalent of the 3D cube. It's intresting but verry hard for me to really underdstand it and stuff. Try google, you'll find something.
Also there's that book about 10 dimensions (with time as the 11th) tough I think it's bullocks really. (also has a website with animations)

[BDC]

Stretched in the 4th spatial dimension.

[Duke Malcolm]

Bah, all this talk of 3 and 4 dimensions is codstwaddle. Everyone knows there is only 2.

[The_Doctor]

I remember watching something that said the 4th dimention is time, lol. Probably some bad sci-fi though and not anything real.

Time is the 4th dimension.

[Scurvy]

time doesnt exist :)

[Silver Rusher]

Time is the 4th dimension.
Err... not really. The other three dimensions are measurements of space, so why would the 4th one be time? No credible argument can back up the claim, but hey, you aren't even providing any kind of an argument at all anyway!

...is this the frontroom? Oh... :oops:

[Bar Kochba]

i think the bottle is more entertaining then the 4D

[Silver Rusher]

i think the bottle is more entertaining then the 4D
Have you seen those weird mugs? Now THEY are confusing.

[The_Doctor]

http://en.wikipedia.org/wiki/Dimension
http://en.wikipedia.org/wiki/Space-time

[Moros]

Time is the 4th dimension.
Time is a property of a universe just like space is one. Both properties have their dimensions. In theory both can have an unlimited number of dimensions, time for example has as far as I know ulimited dimensions. "time doesn't exist." The times, one single time that is the same for anywho anywhere doesn't exist. Time is relative remember that experiment with clocks in a moving train? (or how was it again?) Anyway the amount of space dimensions in our univers is unkown at the moment. Scientist already claim to have discover some with experiments (Zwitserland?) and not so long ago a book and it's site is claimng there'll be 10 dimensions (more based on philosophy then science?) and claims that time is the 11th dimension.

[The_Doctor]

10 dimensions (more based on philosophy then science?) and claims that time is the 11th dimension.

I think that is string thoery.

[Silver Rusher]

The concept of space-time is valid but I think that it is simply changing the definition of dimension. In this context, a dimension is the measurement of the axes of space.

http://dictionary.reference.com/search?q=dimension&x=56&y=15

So while time and space do go hand in hand, I think the association between time and the other three dimensions does not bear enough of a connection for time itself to be called a dimension.

[Ironside]

At first, I thought 'what a sham, they just stretched a cube to make it seem to go into a new dimension, it's still actually just 3-d.' Then I realized, 'no it's actually still just 2 dimensional, as the third is an optical illusion, or perhaps symbolism of depth.' In that sense, stretching the cube of course doesn't make it an actual 4 dimensional object, but with the 4th dimension being time it makes as much sense to let that final stretching represent motion in time as it does to to let the previous one represent motion into a 3-dimensional space.


That's why I never called that object not 4-D as I've got no idea how that illusion would look like. I know it got the basics right. Extending a 3-D cube gives another cube as extra corners so to say. Every time the dimension increases, the edges dubbles in number and an equal strukture forms into the new dimension, like in thier demonstration.

And it's 3 room-dimensions and 1 time-dimension, they're separated you know. Wonders if time is actually only a 0,5 dimension, as so far only forward is known.
Now, make a graphical demonstration of how a particle moves through a 3-D space with time and displaying all the particle positions at the same time. You'll get a "snake" through space but how to represent time? (this is possible by "cheating" ~;p ) .

Now try to image 2-dimensional time :dizzy2: , or better a 10-dimensional space with complex numbers, with 4-dimensional space, making a graphical representation having 24-dimensions :laugh4:

The funny part is that you can calculate on it.

And the formula for a 4-dimensional sphare is 16*pi*r^4/9 and it's volume is 64*pi*r^3/9 and I can prove this :2thumbsup:
Sadly this won't help displaying a 4-D sphare in 3-D, like the drawing of a cube.

[The_Doctor]

The concept of space-time is valid but I think that it is simply changing the definition of dimension. In this context, a dimension is the measurement of the axes of space.

http://dictionary.reference.com/sear...sion&x=56&y=15

So while time and space do go hand in hand, I think the association between time and the other three dimensions does not bear enough of a connection for time itself to be called a dimension.

I see what your getting at, but time is used to measure things (eg, graphs) like the other dimensions.


Now, make a graphical demonstration of how a particle moves through a 3-D space with time and displaying all the particle positions at the same time. You'll get a "snake" through space but how to represent time? (this is possible by "cheating" ) .

Couldn't you just label each particle with a time? I have a feeling this is cheating.

[IrishArmenian]

Wouldn't a 4-D shape shift with time?

[Strike For The South]

Did I tell you my uncle is Armenian?

[ajaxfetish]

And it's 3 room-dimensions and 1 time-dimension, they're separated you know. Wonders if time is actually only a 0,5 dimension, as so far only forward is known.
Now, make a graphical demonstration of how a particle moves through a 3-D space with time and displaying all the particle positions at the same time. You'll get a "snake" through space but how to represent time? (this is possible by "cheating" ~;p ) .

Now try to image 2-dimensional time :dizzy2: , or better a 10-dimensional space with complex numbers, with 4-dimensional space, making a graphical representation having 24-dimensions :laugh4:

The funny part is that you can calculate on it.

And the formula for a 4-dimensional sphare is 16*pi*r^4/9 and it's volume is 64*pi*r^3/9 and I can prove this :2thumbsup:
Sadly this won't help displaying a 4-D sphare in 3-D, like the drawing of a cube.
Personally, my eyes glaze over when string theorists start discussing 10 or 11 dimensions. I understand that mathematically it works and that within the framework of the theory as it now stands they are necessary, but that doesn't lead to cerebral comprehension on my part. I understand that time is different than space though still related, but as I understand it it is accepted as a standard dimension in general scientific practice from Einstein to the present, though naturally with some differences from the spatial realm. As far as trying to represent it in an only 3-dimensional space (frozen in an instant, as it were), I'm not sure there is a good way. And as for trying to imagine multiple time dimensions, :dizzy2: indeed!

Ajax

[Papewaio]

Err... not really. The other three dimensions are measurements of space, so why would the 4th one be time? No credible argument can back up the claim, but hey, you aren't even providing any kind of an argument at all anyway!


Einstein, Special Relativity circa 1905.


Einstein (The Meaning Of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously."

It is a new theory, younger then evolution, so I can understand that you may want to reject this paradigm. It however is essentially modern physics, so if you want to reject it you will also have to reject General Relativity which is the current best explanation of gravity.

[Ironside]

Couldn't you just label each particle with a time? I have a feeling this is cheating.

We have a winner!! :balloon2: :balloon3: :balloon: :party2:

Free beverages of choise for a day ~:cheers: :2thumbsup:


It is a new theory, younger then evolution, so I can understand that you may want to reject this paradigm. It however is essentially modern physics, so if you want to reject it you will also have to reject General Relativity which is the current best explanation of gravity.

It get complicated there, as time is dependant of velocity, who in turn is dependant of space and time. And then is space itself also affected by velocity, atleast fro mthe viewers standpoint. :dizzy2:

While certainly combinable, I'm still not sure if you can call time as the same type of dimension as the 3 space dimensions.

[Rodion Romanovich]

Einstein, Special Relativity circa 1905.

That's a reference, not an argument :wink:



It is a new theory, younger then evolution, so I can understand that you may want to reject this paradigm. It however is essentially modern physics, so if you want to reject it you will also have to reject General Relativity which is the current best explanation of gravity.
I think the theory of relativity is an excellent mathematical model, but apart from calculations it isn't really helpful. Nobody can understand the concept of time being a fourth dimension (especially when the word dimension isn't very well defined and has many different popular definitions) as a way of understanding the universe and making any form of practical real-life reasoning. Just like you didn't say during Newtonian times that mv^2/2 = mgh you would explain the theory with "the kinetic energy is transformed into potential energy". There are simply no similar ways that modern physics models are described in terms other than how the calculation takes place, which IMO makes modern physics an exclusively mathematical and calculation-oriented science. Nobody would say there are imaginary or complex numbered signals going through the wires to your headphones when you're listening to music, however models for audio systems etc. use imaginary and complex numbers for description. The explanations of modern physics are comparable to saying "the signals in the headphones wires are a complex number" as a way of explaining the audio, which would sound pretty absurd. In itself, I don't think the claim "time is the fourth dimension" provides much information for anything else than someone who learns more and uses these model descriptions for carrying out calculations. Together with formulae etc. the statement gets some limited use, however I think just looking at the formulae and thinking of their consequences provided me with a better understanding (however I've forgotten much of the ToR now, since I don't have to read any more physics EVER AGAIN, YAY :jumping: !).

At the very least, I'm personally not any wiser after hearing someone say "time is the fourth dimension", because: 1. the word dimension is ambigiously and imprecisely defined, saying "time is the fourth dimension" is then on the verge of being a circular proof through word redefinition, 2. the theory of relativity, like Newtonian physics and all other models, is based on observations from the time and location scope that we can observe things from, without guarantees that the model will hold for things further away in time and space, and where it's emphasized that it's strictly a model and not an absolute truth that we have

I have no reason to doubt the mathematical accuracy of the ToR for the observations we have seen and also for some that we haven't yet seen (but probably not all of the not yet seen observations), but the statement "time is the 4th dimension" has always struck me as a completely pointless and contentless statement.

===

Re the topic of cool 4D objects, take a look at Salvador Dali's hypercubus crucifiction painting, which is quite interesting (see if you can solve the hidden rebus in it ~:) ):
http://www.goddesschess.com/art%20and%20artifact/dalihyper.html

The cross on which Jesus is crucified is an unfolded 4D cube, unfolded in a way similar to how you would unfold a cube into a 2D paper. I.e. the rebus is that there is an "extra dimension" present. Dali is claimed to have been heavily inspired by the science of the time, including the ToR... Interesting to add to gallery of worthless information :shrug:

[highlanddave]

LegioXXXUlpiaVictrix said

I think the theory of relativity is an excellent mathematical model, but apart from calculations it isn't really helpful.

yes, but the bomb says it works.

[Rodion Romanovich]

LegioXXXUlpiaVictrix said


yes, but the bomb says it works.

oh sorry that wasn't what I meant. I meant apart from calculating - with the work leading to the bomb being one example of such calculation - the ToR (and other modern physics theories) aren't very helpful IMO. The Newtonian physics models are simple, easy to apply, enough accurate for most practical life situations, and they also have a neat philosophical non-mathematical version of explanation. For example a ball flying through the air is said to fall towards earth due to a gravity force so it moves through an arc through a straight universe. However you might as well say it's the ball moving along a straight path while the space is bent in an arc by gravity. The two explanations are equivalent, but Newtonian physics tend to use the more intuitive first one, while quantum physics and the ToR tend to stick to unnecessarily strange explanations like the second one. It probably has it's explanation in that while the Newtonian physics are useful for approximations and intuitive thinking in everyday life, the ToR and quantum physics are solely used by scientists and physics engineers for calculations, where understanding the model in some deeper sense isn't necessary in the same way, so there has been made no effort to make easy and intuitive ways of expressing the formulae in practical everyday world terms.

The other important thing is that neither Newtonian physics nor ToR and quantum physics are facts, they are models. They are made to predict the future, calculate for practical applications, by looking at known applications and making fairly sensible interpolations between them. However since they're all based on observations there is no guarantee that they will be always true outside the location and time scope in which the observations where made. It often happens that the models correctly predict many observations not yet made when the model was made, but there's still no guarantee they'll hold for all time and space. Because "time is the 4th dimension" neither gives any practically useful information nor any deeper understanding of the universe nor is any absolute truth, the statement is IMO empty. The formulae (which inspired the verbal statement that "time is the 4th dimension") are however useful because they give a correct numerical answer for pretty much any observed (by machine or man) phenomenon.

[UltraWar]

Damn, my plan has been thwarted.

[Moros]

this has good animations of 4D objects:
http://darkwing.uoregon.edu/~koch/java/FourD.html

[highlanddave]

LegioXXXUlpiaVictrix, i am not nearly elequent enough in my language skills to describe some of the modern physics applications but i will try.

my brother is a former physics professor so i have listened to him spew out the stuff he works on. two that come to my mind.

he worked on bombarding cotton fiber with atomic elements (sorry can't describe this better) to find the structure of cotton. this was so to help a company that wants to make better synthetic cotton. cotton is apparently very complex. he used the physics you are saying may not be very helpful.

another area he worked on using theory of relativity stuff is cancer treatment at the hospital. he was the guy that would work with a physician to decide a course of treatment and would suggest to the doctor that a patient should get such and such amount of rads and such and such angle for so many treatments to kill the cancer. i forget the exact title he had, but he was pretty important there. he also was responsible using the equations to measure how much the radiation sources had deteriorated over time so that patients would be exposed for the correct amount of time during treatments.

just trying to give you some real world uses of these theories.

[Zalmoxis]

Watched the video a couple of times. I have to say that I'm disappointed, but meh..

[Rodion Romanovich]

LegioXXXUlpiaVictrix, i am not nearly elequent enough in my language skills to describe some of the modern physics applications but i will try.

my brother is a former physics professor so i have listened to him spew out the stuff he works on. two that come to my mind.

he worked on bombarding cotton fiber with atomic elements (sorry can't describe this better) to find the structure of cotton. this was so to help a company that wants to make better synthetic cotton. cotton is apparently very complex. he used the physics you are saying may not be very helpful.

another area he worked on using theory of relativity stuff is cancer treatment at the hospital. he was the guy that would work with a physician to decide a course of treatment and would suggest to the doctor that a patient should get such and such amount of rads and such and such angle for so many treatments to kill the cancer. i forget the exact title he had, but he was pretty important there. he also was responsible using the equations to measure how much the radiation sources had deteriorated over time so that patients would be exposed for the correct amount of time during treatments.

just trying to give you some real world uses of these theories.

yes, I'm aware of many examples where it works. What I'm saying is that you got the formulae which are accurate, you know how to calculate the results, and results you get are correct. But does anybody really understand what they're doing? The mere thought of particles being a sum of waves of different frequencies is very difficult to picture in any meaningful terms, for instance. Just like no voltage can be a complex number but models using complex numbers are excellent for describing voltages in some cases. What I mean is that I don't think anybody can understand reality by trying to understand the intermediary states of the calculations.