Dimensions: A Walk Through Mathematics

Uhh I love this kind of documentaries ! They are soooo inspiring !

Highly recommended to dose yourself with LSD to fully comprehend this documentary. Great documentary that requires an open mind and a good amount of attention. Something most people don’t have without some influence. <('.'’.')><('.'’.')>

@Waldo, you know it always stroke me as odd when people seem to say that 2 dimensions are easier to understand then 4! So they try to explain leap from 2 dimensions to 3, as if 2 dimensions are innately intuitive. The peculiar thing is, no one ever encountered 2 dimensions, because in 2 dimensional plane anything beyond x,y is infinite.

It’s almost impossible to imagine a one dimensional plane as it simply doesn’t exist in any possible way of measure.

As for 4 dimensions, something they didn’t explain is basically in 3 dimensions you have x,y,z which are 90? to each other, and in 4 dimensions you have a new direction t which is 90? to x,y and z.

This doc is rather hard to understand, though very mind boggling! It’s good when you already know the subject, and occasionally thought and imagined it, but it’s impossible to grasp it point blank, I think.

@ iraoksman

Well I can understand two demensions just fine, I can see it in my head. It is just a flat plane like a piece of paper. Of course three demensions are also intuitive to me, I live in three demensional space. But four demension just doesn’t make sense. You can not draw a perpendicular axis for the fourth demension, it is physically impossible. To me the four demensional shapes they drew simply looked as if they included a face inside the three demnsional object. But they said that was just the projection of the object not the actual shape as they could not represent the actual shape in our three demensional world. I’ll get to it in geometry eventually, I am a physics major. Maybe the professor I get can make my hick brain understand. The idea is interesting to me, I am sure it would open my mind to all kinds of possibilities. Thanks for trying to help me though, I am glad one of us got it.

*I dunno if I understand it per say

^^

What makes it both difficult and easy to see is that the projection changes the size of the face and side of the object you are trying to look at just as the projection changed the size of the continents when projecting the three dimensional earth onto a two dimensional plane.

Realize that ninety degrees from x, y, and z is t or time. Put a pen on the table in front of you. Now, what is the difference between the pen you just placed on the table and the one you are looking at now. The one you see now is older than the one you placed there at first. Its’ three dimensions didn’t change at all but it still aged while is was sitting there and it continues to age.

If you could travel at the speed of light, according to Einstein, then time would stop progressing forward and the pen wouldn’t age but you would also stop progressing forward so you wouldn’t be able to tell anyway. Now if you went a little faster than the speed of light the pen would be getting younger as would you. Now a good question would be ‘If you could go back in time to before the pen was made would it still be in front of you or because you have it with you while you are traveling through time it would still be there?’

If time stops at the speed of light then time for light doesn’t exist. While it takes eight minutes for light to get to earth from the sun, that light isn’t eight minutes older than when it left.

It is hypothosized that there is an absolute zero in temperature but not necessarily an absolute maximum temperature. I will put it to you that there is an absolute zero in speed but no absolute maximum even past the speed of light.

Assume there is a galactic center where all matter orriginated from ie. the big bang starting point and you were to stop moving away from that stationary point. You would be at absolute zero speed. As you speed up time slows down so that as you slow down time speeds up and you would age at the fastest rate possible. Now, even if you were to move towards that point as apposed to away from it, as we are now, you would be speeding up from absolute zero and therefore slowing down your time progression.

If the universe stops expanding and begins to contract, we would reach absolute zero time, which would seem to last a very long time as we would age as rapidly as possible with no seeming movement of the earth or stars. We may age a lifetime in a single year or month or week or day. Since we only understand time relative to our own speed/time relationship (which, by the way, is constantly varying) this absolute zero value hasn’t been calculated although it could be.

When the contraction begins, our speed would begin to increase and time would begin slowing down and we would be ageing slower and slower the faster we go but time wouldn’t go backwards as some physicists believe. Time only goes backwards when moving faster than the speed of light (if Einsteins’ calculations are correct).

Thank you for this guys. When I first noticed it my heart leaped with joy like a Salmon making its way through the treacherous Canadian rapids on it’s seasonal migration; Like Santa soaring through the winter skies fuelled on Rum and Cola.

This series makes me want to get out my compass and straight edge and have some fun, Euclid style. If you love mathematics or want to get into the beautiful subject then this documentary introduces some nice concepts and some pretty pictures too.

It is not possible to visualise higher spatial dimensions, but by analogy with flat-world we can see a 3-D part of a 4-D object in our reality of 3 spatial dimensions.

For anyone taking undergraduate Geometry in the future there are a few things to be aware of: firstly that modern geometry courses are the hardest part of a pure math degree, I certainly found that to be true. Secondly, perverse as it may sound, its easier to do modern Geometry analytically (using equations) than Geometrically (using pictures) lest your brain be stretched into a noodle of spaghetti. You may have noticed this feeling while watching this documentary and trying to have a meaningful thought abut it. Lol.

My favourite part of this was the final segment; the proofs hosted by the great German Riemann, although he is dead, and has been for a few hundred years he still managed to roll back time and deliver a rousing proof of stereographic projections. What a man.

Now where did I put that astrolabe?

Ok, great doc. Question to those who know; The recurring spiral patterns within the fractals..Is this a representation of the orrigional equation or a resultant ratio whic occurs? I ask because it reminds me of a documentary about the golden ratio I once watched. And makes me wonder what the base equation would be if one applied that ratio to a fractal and extrapolated backward.
On a less mind boggleing note. The use of Echer in this made me quite happy. He even could have been used when discussinge 4th dementionality as much of his art incorporated it. I got one of those pieces tattooed on me much to the chagrin of the tattoo artest. In fact I think he almost kicked me for screwing with his head, and sued me for giving him carpal tunnel.
The fact that multidimensional math can be seen in advanced artworks makes me believe that somewhere in the depths of the mind is an intuitive knowledge of these things. That implication is very intense if you let it soak in a bit.

Chapter 3 which deals with 4th dimension..

Is it fair to say that every 3d object i see in real life is in fact a 4 dimensional object on the molecular/sub atomic level?

Or is it confirmed that TIME IS the 4th dimension.

If the latter is the case. Does that mean if i sit in a chair my brother just stood up out of, that because moments before HE was there…that it is in fact a 4 dimensional situation we are dealing with?

I’m sorry if my question/explanation is confusing… i am having a tough time comprehending how time fits in.

From my amateur mind I get the feeling if anything time would be the 5th dimension.

Any insight is greatly appreciated.

i really enjoyed this, i might buy the dvd from their site.
are there any other great math documentaries ?

This was… Ok. I feel like some things were drawn out too much, while other ideas weren’t explained enough. For example, the idea of a sphere as a “complex projective line” was interesting but it seems like they just glossed over it, and should have elaborated on it more. This stuff is all really cool but it’s almost too abstract. It would’ve been more enjoyable and enlightening if they’d tried to make it more applicable to real life.

Common on man, what in the world could have been in that comment to warrant it being caught in moderation?

@Waldo; Tool is awesome. look into this one too if you like the way Maynard incorporates math etc. The bonus track of the Tool album 10,000 Days, created by combining “Viginti Tres” and “Wings for Marie” overdubbed with “10,000 Days”. Link here
http://www.youtube.com/watch?v=IPzTuPuq53A
There is allot of Quantum reference in this album as well and it is also fibonacci based.

@Cool E Beans

What I don’t understand is if you are moving past the speed of light and started to move back into time, I believe that would mean you would end up in the same place/time at which you began moving past the speed of light.

In other words… You are at point A at 12:00pm moving at 299,000 km/s then one hour later (1:00PM) at point B you started moving past the speed of light for an amount of time equal to -1 hour, wouldn’t that leave you at the same place/time as point B, therefore proving that traveling back into time further that when you started moving by breaking the speed of light is impossible since you will begin to move backwards and therefore no longer moving forward at the speed of light.

I know all the scientists in the world couldn’t have missed something so trivial so can someone please explain to me how my above calculations are wrong?

Great video, especially, chapter 5 onwards.

@henry
lol.. no i think you actually got it quite right and I never thought about it that way.. although along with opinin I think there is something wrong with making time a physical dimension.. leads to a mess in ur head.

@opinin
I think you might enjoy the series of videos on youtube by user “bgaede” although I disagree with him on the whole “we are the last generation of humans,” i believe you will find the rest of his stuff fascinating to say the least!..

Nothing exists without the fourth dimension which is time. Think of the amoeba. It lives in only two dimensions of left and right and while it has thickness (the third actual dimension) it probably doesn’t have a concept of up or down like we do. But without time passing, there is no living as movement requires time to make the movement. True two dimensional existance is the movie screen. The images have no depth to them at all but again without time passing there is no movement or existance.

@Henry Moving forwards or backwards in time has nothing to do with your position in space. Think of climbing a ladder with rungs on both sides. If you are climbing up one side of the ladder while going slower than the speed of light, reaching the speed of light at the top of the ladder and then going faster than the speed of light while climbing down the other side, you would be able to see yourself climbing up the ladder at the same time that you are climbing down. Now if you got to the top of the ladder and backed back down after crossing the light speed barrior, you would bump into yourself while you are both climbing up and climbing down the same ladder at the same time. I recommend always moving forward when you go faster than light speed unless you really know what you are doing.

@princeton
There is only one of you. If you are traveling faster than the speed of light and see yourself as you move backwards then you are looking at what the real you has already done to get you to the place you are now to see you do it. Think of the ghosts of Christmas past. They are only shadows of what has been. You couldn’t interact with them while you are traveling backwards in time as you would be interacting retroactively. If you stopped moving backwards and resumed progressing forward at Earth time then you could interact with yourself but only if your past self had already met your future self in the past which means you are going to meet yourself. This would create a time loop but only one since past you is going to become future you and future you is not going to replace past you. A self-correcting paradox could occur if your future self eliminated your past self and resumed his/her life from that point on but at each occurence your future self would be getting older and older until death which would be the correction.

There is a good book providing one possible view of time travel called “The Man Who Folded Himself” by David Gerrold. Though I don’t think it actually represents true time travel it is an interesting read.

Picture all of these comments coming from those 2D lizards.
I think Its a good perspective of how we should urge ourselves to understand science.

This is one of the most mind boggling things I have ever came across. If anyone knows of any other docs on the subject that may give you a broader explanation.

I note a few comments here from people who seem to be struggling to “picture” or “imagine” multiple dimensions.

Here’s a litte help: you can’t picture them – we live in a 3 dimensional space, so “picturing” higher timeframes is nigh on impossible with this as our only frame of reference. What you need to do is just understand their characteristics.

For example, picture a person or an object (i.e. a wooden block). It has height, length & width. Now imagine it moving through time – i.e. the block exists on Monday, Tuesday, Wednesday etc. You’ve just visualized a 4 dimensional object.

Higher dimensions work the same way – by adding an additional layer of complexity for each dimension. Imagine 3 blocks existing in 3 separate universes. That’s 9 dimensions. Now imagine them all moving through the same Monday, Tuesday, Wednesday etc. That’s 10 dimensions. Now imagine a string tied around all three universes containing the blocks as they move through time, with the string touching all three universes. That’s 11 dimensions. Got it? Congratualations – you’ve just grasped the rudiments of modern string theory which predicts 11 dimensions (or 9 depending on the theoretical approach used).

Now you have two choices:

1) Go and do a degree in Maths so you can use & understand the tools that predict the theory or…

2) Sit back, smoke a huge joint and just think about it’s implications (^_^).

Good luck!

I hesitate to post because until I press the button, there exist 42 posts, which I find amusing given the topic.

@ren

Here’s a wacky thought. All spaces have subspaces, which I’ll call borders and nodes. In 2D space, lines become borders and points become nodes. In 3D space a 2D space is a border between two 3D spaces and a line is a node or point of intersection between 2 or more borders. By analogy in 5D space, a 3D space becomes a node, analogous to a mere point.

All matter is really energy. Solid objects are a mere illusion. Energy is vibrating in all its possible dimensions. If for an instant a particle’s vibrations in 3D are zero and increase in the fifth dimension, it could reappear anywhere in the 3D universe. Who’s to say exactly how many dimensions our universe consists of or whether or not there are lower and higher dimensional universes? It’s all an endlessly fascinating mindf**k.

@ Ren,

There is no maybe about it, our thoughts can and do move backwards in time and it’s a skill that improves with age. Our thoughts can only move forward in time to speculate over very short periods of time by considering causality: as the fist comes swinging towards your face you know that in the short term future you will feel a stinging pain. Does that count as thoughts moving forward in time? I guess that it is still a speculation because one could dodge the blow or not, but as the time interval becomes smaller and smaller the speculation tends to fact. Lol.

By moving at FTL speeds it has been shown that a persons body can move forward in time. And yet as @Ren said it is physically impossible for us to move backwards in time. Are you still with me?

Thoughts can only move backwards and body can only move forwards in time.

When it comes to temporal quantum movement… Well, anything goes… It’s like a zoo and the animals have all escaped from their cages… Bloody statistics, never give a straight answer to anything.

@ Ren, So in 5-D space all of the 3-D universe is just a point… Nice…

@hugs
that is an interesting take and i’ve heard it before.. I wonder what exactly you mean though.
I don’t agree with all his arguments, but i believe his take on physics is dead on and i don’t think he plays word games, he is just consistent with definitions and points out where people tend to misuse words or rather redefine them to fit their ideas with no regard to what the words actually mean.
i think he gets accused of that same as stefan molineux unfairly. there is no knowledge or communication without concrete definitions that don’t get bent and twisted for convenience.

brilliant documentary.

This has interrested me for a very long time. And I’ve never been able to really get my head around the subject.
I must say this documentary has given me renewed enthousiasm to try and ‘see’ in 4D :-)

What would really interrest me is seeing a ‘shadow’ of a 4D object built in 3D space. And then, using vanishing points (or planes ?) – similar to those we use to create the illusion of 3D on a 2D paper or screen – to create the illusion of 4D in the 3D space.
If Escher were still alive, he would surely be of great help in this area…
What we see in books and on the screen, is really a 2D object giving us the illusion of a 3D object using perspective. So we’re always using the perspective trick to show 3D objects on a flat surface. Maybe losing the perspective and seeing in real 3D, and then using the perspective trick for the 4D to 3D downscaling would work.

Anyone know if this has been attempted/done yet ?
Are there any theories about 4D/3D vanishing points/planes ?

At introduction I think: “of course another Euro-centric history of science.” Why is it Westerners are so obsessed with 1. attributing all science to the Greek, while there is so much literature on science earlier and everywhere else on the globe 2. why they keep thinking they are the Greek’s successor, while the Greeks themselves associated with Asia much more and abhorred Western “barbarians”?

Best math lesson I ever got! I have to rewatch this to understand what the 4th dimension is. All the examples of 4d objects looked 3d… which I think is the point…since we can’t see in 4d… but then what’s 4d and how can anyone explain it if humans only see in 2 dimensions? So many things to follow through on… great documentary.

i see 3d in different shapes, or 1thats without imagination but i still cant see or imagine 4d? what differentiates 3d between 4d?

Maybe I’m doing my usual, over complicating, but if you live in flat land surely you have no horizon, how would you see the stereographic projections. Also silly with the cross sections, you could slice things any number of ways and get a different shape. The music is irritating and the man is too slow :)

Redundant Double Post :(
Math Rules.

The reason you can tell that a ball is round and not just a flat circle plane, is light.

The reason you can tell that a box is not just a square plane, is light AND size (the edge furthest away seems the smallest)

That’s basically how we perceive 3D, off course stereo-vision enhances our our perception, you could argue that sound also enhances our 3D perception

dimention cero is a point
1st dimention is a point in movement, a line
2nd dimention is a line in movement, a surface
3rd dimention is a surface in movement, a volume
4th dimention is a computericed movement of 3rd dimention
so what