Original Post
I''ve read the monkey thread, and here are my comments (If you want the topic right now, switch to the next section):
Section 1 - Toads
Impressive I must say... And if we try this with Toads... An infinite number of Toad with typewriters is very likely to happen to type the good letters to write all the Shakespears works in the time it takes to type a page. Here is why: Say we have 750 letters in a page, and it takes 1 hour to type a page (randomly, because toads can''t read...). So the possibilities for every letters in this same page is 70**750 (70 power 750, 70 because I concider there are about 70 characters with pontuation and capitals). This is quite a large number, and cannot be calculated with the Windows Calc (no I haven''t tried). That means one thing: if we possess 70**750 toads and every toad doesn''t write the same page, then we would have every possibilities of a single page. Unfortunately, it is very unlikely they will write all of them different pages, so just say we have 70**10 (approximately) toads with the same pages, per pages, that would make 70**760. Now with EVERY possibilities of a page, that means we could have everyone''s work on this planet done... and maybe it could get creative with pages starting with "AFJasdlkjw9AFGHqirlsamdoWTAS"... So Shakespears work could even been done with less than infinite number of toads and typewriter, but by laws of physics you need a typewriter by toad.
Section 2 - Dimensions
This introduction was necessary because the topic of Dimensions was brung in another thread (monkey...). Now here are the REAL dimensions defined by scientist: 0D - Possess an orientation. That''s all. 1D - As 0D, with a length. A Vector, the direction being defined by the sign of the length (negative or positive). This shape cannot be curved because if it did, it would make it impossible to put in a 1D plane, but would rather need a 2D plane to draw it. 2D - As 1D, but it defines an area. A single form. Not necessarly a square or a circle. This form cannot be curved in the third dimension as well. 3D - An object in 3D is defined as a 2D form that possess a volume. This volume must be calculable, although sometimes it gets harder (infinite is still calculable, uh?). 4D - This is where all of you hurt, I think
. Simply, fourth dimension is mentionned as Time, in real world. Although time is not concidered a real dimension (I still believe time doesn''t exist, ok?), it is a popular belief that Time is the fourth dimension. Impossible to draw on 2D support.
5D, 6D, ... - What''s next? Simple. If you believe into multiple universe (a multiverse), then those can come handy by bringing a 1D, 2D, 3D and even 4D universe array 
(don''t think all the Universes will stand in a single 1D array).
PS: The dimensions described here are Real World dimensions. I mean by that that if you are using dimensions mathematics, you won''t necessarly use those dimensions definitions. As a 3D matrix in a computer program is not necessarly a 3D image...
Note that the position for each is defined as (a + bi), a complex number, for each dimension. That is, for an object in 3 dimensions, position is defined like (a+bi,c+dj,e+fk)... For complex number, do a search. They are not necessary if b,d and f equal 0, and aren''t used very often, and almost never in computing.
Cartesian versus Polar coordinates: Ok... Cartesian are defined like you have all learnt in school: right lines defining the axis. For the first 3d dimensions, it''s quite easy. For the fourth dimension, you will have to think about an axis that goes perpendicular to all other lines. It is unfortunatly undrawable (Although it CAN be drawn, we percept things in 3D, making it unperceptable).
Polar coordinates are a bit hardier to understand. They contain the same number of coordinate (1 for 1D, 2 for 2D, ...), but they are defined by angles within a circle, and the axis are circles. To draw a polar plane in 1D, you''ll need a 2D support. For a 2D coordinate, you''ll need a 3D support. For 1D, simply draw a circle and draw from angle to angle. For 2D shapes, you will need to draw the first coordinate first, then draw another circle perpendicular from this coordinate to draw the second dimension... for 3D-polar coordinate, you''ll need to do the first 2D and then draw a circle perpendicular to the other 2, and find the last coordinate... Still, you cannot draw into 4D (unless you are VERY VERY good drawer 
)
All dimensions can be drawn in planes of further dimensions (a 2D form can be drawn in 3D, and a 0D position can be understood in 4D). All the other aspects of the bigger dimensions are concidered 1/oo (infinite). For example, the second dimension (area) of a 1D shape is concidered 1/oo, as the fourth dimension (time) on a 3D shape is 1/oo.
That''s all I hope you learned or at least find something cool in it. Don''t want to write this all for nothing. Post here anything you have to add
Section 1 - Toads
Impressive I must say... And if we try this with Toads... An infinite number of Toad with typewriters is very likely to happen to type the good letters to write all the Shakespears works in the time it takes to type a page. Here is why: Say we have 750 letters in a page, and it takes 1 hour to type a page (randomly, because toads can''t read...). So the possibilities for every letters in this same page is 70**750 (70 power 750, 70 because I concider there are about 70 characters with pontuation and capitals). This is quite a large number, and cannot be calculated with the Windows Calc (no I haven''t tried). That means one thing: if we possess 70**750 toads and every toad doesn''t write the same page, then we would have every possibilities of a single page. Unfortunately, it is very unlikely they will write all of them different pages, so just say we have 70**10 (approximately) toads with the same pages, per pages, that would make 70**760. Now with EVERY possibilities of a page, that means we could have everyone''s work on this planet done... and maybe it could get creative with pages starting with "AFJasdlkjw9AFGHqirlsamdoWTAS"... So Shakespears work could even been done with less than infinite number of toads and typewriter, but by laws of physics you need a typewriter by toad.
Section 2 - Dimensions
This introduction was necessary because the topic of Dimensions was brung in another thread (monkey...). Now here are the REAL dimensions defined by scientist: 0D - Possess an orientation. That''s all. 1D - As 0D, with a length. A Vector, the direction being defined by the sign of the length (negative or positive). This shape cannot be curved because if it did, it would make it impossible to put in a 1D plane, but would rather need a 2D plane to draw it. 2D - As 1D, but it defines an area. A single form. Not necessarly a square or a circle. This form cannot be curved in the third dimension as well. 3D - An object in 3D is defined as a 2D form that possess a volume. This volume must be calculable, although sometimes it gets harder (infinite is still calculable, uh?). 4D - This is where all of you hurt, I think
. Simply, fourth dimension is mentionned as Time, in real world. Although time is not concidered a real dimension (I still believe time doesn''t exist, ok?), it is a popular belief that Time is the fourth dimension. Impossible to draw on 2D support.
5D, 6D, ... - What''s next? Simple. If you believe into multiple universe (a multiverse), then those can come handy by bringing a 1D, 2D, 3D and even 4D universe array (don''t think all the Universes will stand in a single 1D array).
PS: The dimensions described here are Real World dimensions. I mean by that that if you are using dimensions mathematics, you won''t necessarly use those dimensions definitions. As a 3D matrix in a computer program is not necessarly a 3D image...
Note that the position for each is defined as (a + bi), a complex number, for each dimension. That is, for an object in 3 dimensions, position is defined like (a+bi,c+dj,e+fk)... For complex number, do a search. They are not necessary if b,d and f equal 0, and aren''t used very often, and almost never in computing.
Cartesian versus Polar coordinates: Ok... Cartesian are defined like you have all learnt in school: right lines defining the axis. For the first 3d dimensions, it''s quite easy. For the fourth dimension, you will have to think about an axis that goes perpendicular to all other lines. It is unfortunatly undrawable (Although it CAN be drawn, we percept things in 3D, making it unperceptable).
Polar coordinates are a bit hardier to understand. They contain the same number of coordinate (1 for 1D, 2 for 2D, ...), but they are defined by angles within a circle, and the axis are circles. To draw a polar plane in 1D, you''ll need a 2D support. For a 2D coordinate, you''ll need a 3D support. For 1D, simply draw a circle and draw from angle to angle. For 2D shapes, you will need to draw the first coordinate first, then draw another circle perpendicular from this coordinate to draw the second dimension... for 3D-polar coordinate, you''ll need to do the first 2D and then draw a circle perpendicular to the other 2, and find the last coordinate... Still, you cannot draw into 4D (unless you are VERY VERY good drawer )
All dimensions can be drawn in planes of further dimensions (a 2D form can be drawn in 3D, and a 0D position can be understood in 4D). All the other aspects of the bigger dimensions are concidered 1/oo (infinite). For example, the second dimension (area) of a 1D shape is concidered 1/oo, as the fourth dimension (time) on a 3D shape is 1/oo.
That''s all
I hope you learned or at least find something cool in it. Don''t want to write this all for nothing. Post here anything you have to add
Programming is:
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