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kira506

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- Thread starter kira506
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kira506

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Khashishi

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There are more sophisticated definitions of dimension if you are interested. The volume of a ball increases with the radius of the ball proportional to the radius^dimension. A 1D object acts as a boundary in a 2D shape. A 2D object acts as a boundary in a 3D space. A 3D space acts as a boundary in a 4D hyperspace, or manifold.

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Pythagorean

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- #4

kira506

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There are more sophisticated definitions of dimension if you are interested. The volume of a ball increases with the radius of the ball proportional to the radius^dimension. A 1D object acts as a boundary in a 2D shape. A 2D object acts as a boundary in a 3D space. A 3D space acts as a boundary in a 4D hyperspace, or manifold.

Thank you so much ! Now I understand , the boundaries example helped me a lot along with the radius part , now I'm kinda able to visualize it c: thanks a lot !

- #5

kira506

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hehe , may be , but me and my brother keep obssessing over them dunno why ! We're so fascinated by the thought of the presence of multi-dimensional planes ! Thank you though , the definition really helped me in forming the image in my brain c:the4th dimension". We have three spatial dimensions. They are neat because they are independent of each other (orthogonal... at 90 degree angles from each other). There's nothing inherently special about dimensions.

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meBigGuy

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Considering spatial dimensions you should think in terms of right angles (actually othogonality). 1 dimension is a line. 2 dimensions is a right angle to the 1st line (creating a plane). 3 dimensions is a right angle to both lines, creating the corner of a cube (3 orthogonol dimensions). 4 dimensions is a right angle to all three lines (impossible in the 3 dimensional world), creating the corner of a tresseract (google "tesseract" and "klein bottle"). There is no limit to how far you can go with spatial dimensions.

Based on this, try to think about a 4 dimensional chess board and see if your brain explodes.

Obviously we can only see a tesseract it terms of its 3 dimensional or 2 dimensional projection. This is in much the same way we view the projection of a cube on a 2 dimensional piece of paper.

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HallsofIvy

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To label points on the floor of the room you are sitting on uniquely, we could measure the distance from one wall and the distance from another wall at right angle to the first. Two numbers, so that is two dimensional. To label points any where in the room, we could drop a line from the point perpendicular to the floor. The two numbers identifying the point on the floor, together with the height from the floor, uniquely identify that point. Three numbers, so three dimensions.

Physicists study "events"; things that happen at a specific location at a specific time. It takes, of course, three numbers to identify the location and a single number to specify the time. A total of four numbers so the "world of physics" is "four dimensional".

(I remember watching the very first "Dr. Who" episode, "An Unearthly Child". (No, not its first airing!)

The Dr's Granddaughter, who is a student in an earth secondary school objects to her teacher talking about "four dimensions" saying "what about the fifth dimension?". When asked what the "fifth dimension" is, she responds "space"! That's the problem having dialog for "advanced beings" written by not-so-advanced beings!)

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kira506

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Considering spatial dimensions you should think in terms of right angles (actually othogonality). 1 dimension is a line. 2 dimensions is a right angle to the 1st line (creating a plane). 3 dimensions is a right angle to both lines, creating the corner of a cube (3 orthogonol dimensions). 4 dimensions is a right angle to all three lines (impossible in the 3 dimensional world), creating the corner of a tresseract (google "tesseract" and "klein bottle"). There is no limit to how far you can go with spatial dimensions.

Based on this, try to think about a 4 dimensional chess board and see if your brain explodes.

Obviously we can only see a tesseract it terms of its 3 dimensional or 2 dimensional projection. This is in much the same way we view the projection of a cube on a 2 dimensional piece of paper.

It explodes everytime I try to think about it , taht's why I imagine it as a cube enveloppping the other 3 dimensions and perpendicualr to each , that's why time is the first candidate , it kinda envelops them in my opinion , I'll google them , and I'm sure my mind will explode even more than before xD and I'll have to reassemble my concept once again

- #9

kira506

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To label points on the floor of the room you are sitting on uniquely, we could measure the distance from one wall and the distance from another wall at right angle to the first. Two numbers, so that is two dimensional. To label points any where in the room, we could drop a line from the point perpendicular to the floor. The two numbers identifying the point on the floor, together with the height from the floor, uniquely identify that point. Three numbers, so three dimensions.

Physicists study "events"; things that happen at a specific location at a specific time. It takes, of course, three numbers to identify the location and a single number to specify the time. A total of four numbers so the "world of physics" is "four dimensional".

(I remember watching the very first "Dr. Who" episode, "An Unearthly Child". (No, not its first airing!)

The Dr's Granddaughter, who is a student in an earth secondary school objects to her teacher talking about "four dimensions" saying "what about the fifth dimension?". When asked what the "fifth dimension" is, she responds "space"! That's the problem having dialog for "advanced beings" written by not-so-advanced beings!)

Rofl XD yeah , because the other 3 dimensions are not enough for space , si ,I kinda agree with them too , time is the non-spatial dimension accompanying the 3 dimensions or any nth dimension which appears and it will be no.s indentifying location of dimensions * time , thank you so much for the explanation c:

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meBigGuy

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It explodes everytime I try to think about it , taht's why I imagine it as a cube enveloppping the other 3 dimensions and perpendicualr to each , that's why time is the first candidate , it kinda envelops them in my opinion , I'll google them , and I'm sure my mind will explode even more than before xD and I'll have to reassemble my concept once again

The spatial dimensions are orthogonal and fundamentally independent. I don't see time as being analogous. If you had 5 spatial dimensions, they could all independently vary in time.

Regarding "enveloping", I have similar philosophical musings, that moving in time is somehow perpendicular to the three spatial dimensions. But, I don't think they are sound.

I see a conflict in that I can play 2,3,or 4 dimensional chess and the game requires time. In the physical world, spatial dimensions are just plain different than time.

http://www.math.uiuc.edu/~reinige1/Chess/chess-basicmath.pdf is interesting.

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Chronos

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- #12

Pythagorean

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But to visualize a state trajectory through 4 dimensions isn't terribly easy with the book analogy.

- #13

kira506

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I guess you're right , time varies with all dimensions and doesn't define their shape , thanks for correcting me :DThe spatial dimensions are orthogonal and fundamentally independent. I don't see time as being analogous. If you had 5 spatial dimensions, they could all independently vary in time.

Regarding "enveloping", I have similar philosophical musings, that moving in time is somehow perpendicular to the three spatial dimensions. But, I don't think they are sound.

I see a conflict in that I can play 2,3,or 4 dimensional chess and the game requires time. In the physical world, spatial dimensions are just plain different than time.

http://www.math.uiuc.edu/~reinige1/Chess/chess-basicmath.pdf is interesting.

- #14

kira506

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Thaaanks , it facilitates visualizing how we can add up dimensions but as simple is it might sound , still visualizing them together is difficult but thanks c:

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- #15

kira506

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But to visualize a state trajectory through 4 dimensions isn't terribly easy with the book analogy.

I agree with you on this one

- #16

meBigGuy

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Spatial dimensions are but one example. For spatial dimensions, each variable represent an orthogonal physical space. Dimensions 1,2 and 3 are pretty easy to visualize (look at the vertex of a cube). Dimension 4 is orthogonal to the vertices of a cube, so is somewhat imaginary in our world and difficult to visualize.

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