Two questions

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Two questions

Postby Shogun » Sun Dec 07, 2008 4:31 pm

Double the questions, double the fun!

1. My knowledge of maths/geometry is pretty limited, so I don't quite understand a couple of things. In your description of a 1D object (and in fact anything larger than 0D), you refer to it as an object made of points (0D objects), which are infinitly small. Now, if a point is infinitly small (and by the way, does "infinitly small" mean absolute zero, or approx. (~) zero? ...or neither?), then how come that when you combine several points together, they become meausrable objects (lines)? Surely zero plus zero will always remain... zero? I don't follow the logic.

2. According to modern science, are there 4D or even bigger-dimensioned objects in our universe? (I'm not talking about the spacetime continuum where time is the fourth dimension.)

...and one ultra-tangled bonus question: Whenever Fred sees a sphere, he will view it as demonstrated in here. Whenever Bob sees a sphere his brain will process it using his 2D view. Whenever Bob sees a tetrasphere he will view it as demonstrated in here (a sphere emerging out of nowhere, growing, shrinking and disappearing). But how will Bob, our 3D friend, react to a "quintesphere" - a 5D sphere? (Surely he won't see a tetrasphere doing the grow-shrink thingy, since he cannot grasp tesseracts?) And when 4D Emily sees a quintesphere, will she see it as a tetrasphere appearing out of nowhere, growing, shrinking and disappearing?
I've been trying to do projections of this in my head but I could use some help.

P.S.: This is a great website and I'd like to kudos its owner(s) for hosting and updating it.
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Re: Two questions

Postby papernuke » Fri Dec 12, 2008 3:45 am

viewtopic.php?f=3&t=1237
there is a thread on this
"Civilization is a race between education and catastrophe."
-H.G. Wells
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Re: Two questions

Postby Keiji » Fri Dec 12, 2008 9:10 am

As for the rest of your questions, sorry I didn't reply to them earlier - I read the topic and then got interrupted before replying, and forgot about it as the highlight disappeared :oops:

Shogun wrote:2. According to modern science, are there 4D or even bigger-dimensioned objects in our universe? (I'm not talking about the spacetime continuum where time is the fourth dimension.)


Sadly the answer is no. The scientific theories that have more than three dimensions (excluding time) have only additional dimensions that are treated differently from our three spatial ones. I'm not entirely sure on the details as I've never really looked into these theories much, but the real universe has never been considered to have more than three Euclidean spatial dimensions.

But how will Bob, our 3D friend, react to a "quintesphere" - a 5D sphere? (Surely he won't see a tetrasphere doing the grow-shrink thingy, since he cannot grasp tesseracts?)


If you pass a pentasphere through a realm, this is akin to passing a 3D sphere through a line. So he would see a sphere growing and shrinking, but there are lots of ways to pass the pentasphere through, so he may see it growing and shrinking in an odd pattern depending on the exact movement of the pentasphere.

P.S.: This is a great website and I'd like to kudos its owner(s) for hosting and updating it.


You're welcome! I currently host and maintain the forum as the original owner has been too busy to attend to it for... seems like forever :]
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Re: Two questions

Postby Max88831 » Sun Jan 04, 2009 3:28 pm

1. My knowledge of maths/geometry is pretty limited, so I don't quite understand a couple of things. In your description of a 1D object (and in fact anything larger than 0D), you refer to it as an object made of points (0D objects), which are infinitly small. Now, if a point is infinitly small (and by the way, does "infinitly small" mean absolute zero, or approx. (~) zero? ...or neither?), then how come that when you combine several points together, they become meausrable objects (lines)? Surely zero plus zero will always remain... zero? I don't follow the logic.


Well the thing is in each dimension your degree of freedom increases, this means in the 1st dimension you can only move back and forth. In the 2nd Dimension you have the digree of freedom to move on a plane in back and forth and left to right. THen in 3rd Dimension you are able to move 3 different degrees of freedom, this is back and forth, left to right and up and down. In your case it means that the object is moving from one point to another through a straight line in a motion thats either back or forth.

Infinately small means that the number is a so called "never ending" integers with an infinite amount of digits. Now I dont believe in a infinite number but in mathematcal terms the term infinite means a number that is beyond calculation so we might be able to calculate to 100 trillion digits while the so called infinite number has 100 trillion and one digits and there we assume the digit is infinite.

Ok so this is the deal when you connect several points to create a line it is still a 1D object is very interesting and there is an easy explanation.
THe dimensions are based on degrees of freedom set by a creature within that dimension.
SO imagine a rollercoaster, the rollercoaster car can only go in 1 set of freedom which is back and forth. THis makes it a 1D movement. Now when we add twistes and turns to the rollercoaster tracks it still will only have the movement of back and forth, this means that even it it travels from point to point in a line, the rollercoaster still can only go back and forth making it a 1 Dimensional movement and object even if it is in a 3D world for example.
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