| Our material universe is merely the intersection of tangled world lines of geodesics in a four-dimensional continuum. |
| For the extreme pathway matrix of this system, there are four singular values, indicating a four-dimensional cone residing in the nine-dimensional flux space. |
| Attempts have been made to construct drawings and models showing a four-dimensional body. |
| Fortunately, in living systems certain conditions must be fulfilled for three-dimensional bodies to occur in four-dimensional space. |
| The theory that Paul described in particular involves a four-dimensional space plus one time dimension, which he called the bulk. |
| I regret that it has been necessary for me in this lecture to administer such a large dose of four-dimensional geometry. |
