The Fourth Dimension
By: Mohammed alqahtani
CS525 – spring 2010
The fourth Dimension was studied by Scientists, Psychologists, Philosophers ,Spiritualists ,Mathematicians and Physicists since the 1800s .The point trying to use to explain some of the universe .At the beginning , the logic was to make the 3D to rotate around its image or itself .Some Scientists considered the time as a dimension beside the other three , However ; this theory mathematically is not correct .We need real dimension to consider it as new dimension .Before we go the fourth dimension ,let’s go over the previous to know we came up with it .
The first Dimension :
The first Dimension “1D” world is like a piece of string. There is only one axis along which one may move along this string, the X-axis. The 1D object have one fundamental unite is length, because there aren't any other dimensions to accommodate width or height. So the only possible objects in 1D are points, which are 0D, and lines, which 1D.
Picture1 : Diagram explains the 1D
The Second Dimension :
The Second Dimension world is a plane, like the surface of a piece of paper, The 2D object has two fundamental unite : width and length . So that The 2D world is much more interesting than the 1D world, because a much larger variety of objects are possible.
Picture2 : Diagram explains the 2D
The third dimension :
The Third Dimension world are bounded not by lines or curves, but by 2D surfaces., The 3D object has three fundamental unite : width , length and height. So that The 3D world is much much more interesting than the 1D , 2D world, because a much larger variety of objects there . For example, a cube is bounded by 6 squares, and a ball is bounded by a spherical surface. The spherical surface is 2D .
Picture 3 : Diagram explains the 3D
Now, We can emerge the objects of any dimension , The rule we see that in N dimensions, objects are bounded by (N-1)-dimensional boundaries. in 1D are bounded by 0D points; objects in 2D are bounded by 1D and objects in 3D are bounded by 2D surfaces
The Fourth Dimension :
The fourth Dimension axis wich goes throu the Z,Y and Z , The 4D object has four fundamental unite : width ,length heights and 4thD which is W .for example a hypercube has a length, width, height and a fourth dimension that is perpendicular to all three of the other units.
Picture 4 : Diagram explains the 4D
What we see in our life ? Our universe is 3D , our eyes actually only see in 2D. Our retina has only a 2D surface area with which it can detect light coming into our eye.So the picture we see is not 3D, but a 2D projection of the 3D universe we are looking at, the shadows help to image the 3D picture. Simply the 4D seeing is the ability to see or watch 3D inner picture from inside another 3D object, in other words, the ability to the red small box at the above picture through the bigger one.
Picture 5 : explanation of how we see our universe
So in higher level our eyes can’t see the 4D picture normally but there are some technologies help human eyes see the 4D picture ,However ; the picture we will see then is 3D being project of the 4D objects .
Picture 6 : explanation of how we our eyes receive the 4D picture
Do we need this ? we Why even care ? Some application use the fourth dimension for useful aims and in our life , we will see later in this paper .Mostly , they aims to see the inner 3D objects which is inside the 4D, beside the endless curiosity of the scientists.
4D cinema is 4D application or being ? No , it isn't really 4D ,it’s combination of 3-D film with physical effects synchronized with film in the theatre to make the move more excitedfor example , i.e. 4D Avatar.
Picture 7 : Small 4D theater with physical effects
Current 4D application
4Ultrasounds
Ultrasound technology was invented in 1987 .4Ultrasoundsis a medical test use the frequencies of the sound waves to create a 3D image of inner organs inside the body .4Ultrasoundsis is used very often to picture the baby during the pregnancy .A 4D ultrasound uses a sonogram machine to take images from different angles for the organs for example in the baby case it could give picture of the face or picture help us to know the gender of the baby , age , recognize the body parts. Also it can give a live picture for the movements that the baby makes during the imaging process.
4D ultrasounds simple and easy to use “not necessary to be a doctor”. To set up the imaging process ,it would take approximately twenty minutes , one hour for the whole process .4D ultrasounds is considered as a safemachine if it use regularly with the right directions and guidelines , there is nothing should be avoided with we use it .
Picture 8 : images from different angles taken for a baby by 4D ultrasound
How ultrasound can send 3D object picture. The machine send the sound waves forward inside the body at different angles then it processes returned echoes by computer program based on a the mathematical theory of 4D .Then crating the image based on that.
4D radiotherapy
What is 4D radiotherapy? According to 4D Radiotherapy PanelASTRO 2003 .it ‘s The explicit inclusion of the temporal changes in anatomy during the imaging, planning and delivery of radiotherapy .Radiotherapy : aimed to use cancer’s treatment to treat or help to discover .Most common cancer types . Based on the tumor type, location, and stage , health conditions of the patient.The process of 4D Radiotherapy:
•4D CT imaging:gaining a sequence of CT image sets over phases sequences of a breathing cycle.
•treatment planning : creating a plan , how to set the CT image acquired for every phase .
•4D Treatment Delivery : Continuous delivery of the 4D treatment plans throughout the breathing cycle .
Picture acquired by 4D CT. explain The tumor at lung is highlighted in red.
Finally most of the fourth dimension application are trying to explore the inner objects of 3D , see what is inside whether it was human body or building …. Etc .one of them Tracking and Data Fusion for 4D Visualization.There are many applications but its not really applied , they still under the test .
References
- Fourth Dimension and Non-Euclidean Geometry in Modern Art - by Linda Dalrymple Henderson.
- Cubism and the Fourth Dimension - Elijah Bodish
- Automatic re-contouring in 4D radiotherapy - Weiguo Lu1, Gustavo H Olivera .
- 4D Euclidean space -
- The Fourth Dimension -By Charles H. Hinton
- Art in the Fourth Dimension - Runette Kruger
- Multimodal Exploration of the Fourth Dimension - Andrew J. Hanson∗ Hui Zhang
- The Fourth Dimension - Eugen Schweitzer
- Ultrasound Characteristics of the Uterus in the Cycling Mare and their Correlation with Steroid Hormones and Timing of OvulationBy Dr. Jonathan F Pycock, B.Vet.Med., Ph.D., D.E.S.M., M.R.C.V.S.
1 / M.alqahtani – spring 2010