# For all you 3d thinkers out there.

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say what
 derp 67% [ 4 ] lol 33% [ 2 ]

Zwapp
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04 May 2014, 5:23 pm

Here goes, I'm currently sleepless because I got started thinking about dimensions, and why we only percieve 3 spatial ones.

it started simple, make a point and another point and draw a line between them, now you have one dimention, pretty simple so far.
do note that if you were to make two other points and draw a line that is not parralell to my original line it would still be one dimension, just a different one, it all depends on you defining the line as the baseline dimension, it matters later on.

so now you have one dimension, lets make another one, you'd most often think to draw a new line in a 90 degree angle from the first, but that just makes further explaining more tedious, so we'll do it the proper way instead.
instead of thinking about the first line as point A to point B, think of it as a continous series of points going from point A to and beyond point B, and equally from B to and beyond A.
what we do next is make a new "line" parralel to the first, and again, and again, etc.

Now we have two dimensions of points lined up, like a paper covered in dots, so far so good.
we now have a simple recipe for the third dimension, a paper with dots on top of the first paper, and so on.

Now I want to return to the line at 90 degrees model, just because that's how I had it in my head at the time.
Imagine this model, three lines all at 90 degrees from one another, and put it in a box, now make an identical box and place it next to the first box, make another one and another one and so on and we got outselves the fourth dimension.

WELCOME
You made it this far, well done, that was the intro.
in school we used x,y,z to determine coordinates on a 3d model, but because I'll be talking about a 4d model I'll use A,B,C,D instead.
remember the two one dimensional lines I mentioned at the start, the point I wished to make was that there is no "first" direction unless we define one, any three of the 4 dimensions we made so far can be the spacial ones we can percieve, and that is why I can't sleep right now.

So now lets make an experiment, take point A2,B3,C4 on a 3d model, simple, trace A to 2, then B to 3, then C to 4, there you go.
Or trace B to 3 first, then A to 2 and C to 4, or any other combination for that matter, it all ends in the same location.
Now look for A1,B2,C3,D4 on a 4d model, can we, like in the 3d model, trace from any dimension first?
in my sleepy brain, no, I have to start with D, look for cube number 4, and then proceed with the 3d model inside.

If you are not yet tired of pondering about the above text, feel free to do so for a while, I'll bold the next step so you'll find it easily
Lets take it a step further, and add another dimension, we left off with a line of cubes with a 3d model inside, and because I taught us the proper method before, we can easily add another dimension by making a new line above the first, again and again, we now have 5d, lets make more, lines of cubes on top of those cubes, now we got a big rubics cube, that's also 6 dimensions.

But wait, it looks kinda similar to the dots of the first three dimensions, in fact, lets just shrink all the cubes into points and make the new 6d model look exacly like the 3d model and call the last 3 dimensions the ones we can see everyday.
I have no Idea what I can accomplish with this as of this moment but it's a funny thought.

and since we have a 6d model disguised as a 3d model, let's put it in a cube and copy it, a line of 6d cubes becomes 7d, now we continue the same steps as before and add lines, then lines of lines to have 9 dimensions, neat.

Here comes the biggie, suppose the 9d model A,B,C,D,E,F,G,H,I and define dimensions A,D and G as the spatial dimensions we see in the everyday life.....
Now I'm going to bed

cberg
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04 May 2014, 10:27 pm

Arbitrary dimensionality is an amazing thing. If you'd like to render your thought experiments, I suggest d3.js, it's a beautiful animated graphing framework capable of output to basically any type of display, with proper code support that is. I agree with you entirely, Brunileschi perspective is completely illusory.

https://github.com/mbostock/d3/wiki/Gallery

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cberg
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04 May 2014, 10:30 pm

Side note; before he passed, my Norsk grandfather was a mathematician, professor and even a boatbuilder. He taught me non-euclidean geometry and I believe that's what led me to my data science interests today.

My name is on Ellis Island, if I lived in Norway I would be Karl (I'm a 4th generation Charles Bergren) and thus I am quite jealous of your situation, whatever that may be. I love the north and if I can't move to Sweden I want to at least spend time in Canada.

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"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

cberg
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05 May 2014, 12:51 am

Furthermore, the 'flattened' stages of your hypothesis provide a solid basic understanding of ternary logic. The early stages of the experiment represent Boolean thought.

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

Zwapp
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05 May 2014, 5:06 am

good morning, thanks for the replies.

I keep thinking that this compressing method is going about it wrong, by the same logic i can compress a line to a point and make a new line with those points, giving a whatever-d line..

as for the big one I posted at the end of my post, I believe it was a stupid thing to say, considering how i can make a 2d plane align with either A,B or B,C in a 3d model, or something like that.

eric76
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05 May 2014, 9:38 am

cberg wrote:
Side note; before he passed, my Norsk grandfather was a mathematician, professor and even a boatbuilder. He taught me non-euclidean geometry and I believe that's what led me to my data science interests today.

My name is on Ellis Island, if I lived in Norway I would be Karl (I'm a 4th generation Charles Bergren) and thus I am quite jealous of your situation, whatever that may be. I love the north and if I can't move to Sweden I want to at least spend time in Canada.

When my great grandparents came to the US from Norway, they changed their last name to something more American. I think it was something like "Zinneson" before but I'm completely unsure of the spelling". I think that they were originally from some small village near Stavanger.

eric76
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05 May 2014, 9:43 am

I have had dreams in the past in which I was convinced (during the dream) I was dreaming in four dimensions and was awestruck at the mathematical beauty of what I saw.

Aldedebaran
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05 May 2014, 10:46 pm

This guy explains something called the "Point-line plane conjecture." Which is quite similar to what you described. Using this model it is easy to grasp up to ten dimensions. The fourth dimension is time. It gets weird at higher dimensions and manipulating even simple shapes in 4 dimensions is a cool cool thing to develop.

eric76
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06 May 2014, 12:56 am

Has anyone hear read Edwin A Abbott's Flatland" A Romance of Many Dimensions?

See http://eric.gruver.net/g201.html

eric76
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06 May 2014, 1:21 am

Aldedebaran wrote:
The fourth dimension is time. It gets weird at higher dimensions
The fourth dimension in the real world is time.

In mathematics, there is no requirement that any dimension be that of time. Rather, it is just an additional dimension.

Quote:
manipulating even simple shapes in 4 dimensions is a cool cool thing to develop.
It's actually quite difficult to picture. About the best one can really do is to imagine a 4-dimensional space projected into a 2-d space and see what happens in the projection as you move a 4-dimensional object around in that 4-dimensional space.

Remember that what we see of our 3-dimensional space is really 3-dimensional space projected onto a mathematical 2-dimensional space by the lens of our eyes.

cberg
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06 May 2014, 7:04 am

eric76 wrote:
I have had dreams in the past in which I was convinced (during the dream) I was dreaming in four dimensions and was awestruck at the mathematical beauty of what I saw.

Dreaming in code is fun... The language isn't constrained to technology.

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

cberg
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06 May 2014, 10:20 am

Zwapp wrote:
good morning, thanks for the replies.

I keep thinking that this compressing method is going about it wrong, by the same logic i can compress a line to a point and make a new line with those points, giving a whatever-d line..

as for the big one I posted at the end of my post, I believe it was a stupid thing to say, considering how i can make a 2d plane align with either A,B or B,C in a 3d model, or something like that.

Ternary logic charts overflow two dimensions, they're inherently abstracted. Personally I don't see the rationale in reasoning beyond dimensionality one is able to manipulate outside of cryptography, but it's plenty of fun to try. I like rotational algorithms

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos