Quotes About Four-dimensional

As a matter of fact we live in a world in which non-identity is as entirely general as gravitation, and so every identification is bound to be in some degree a mis-evaluation. In a four-dimentional world where 'every geometrical point has a date,' even an 'electron' at different dates is not identical with itself, because the sub-microscopic processes actually going on in this world cannot empirically be stopped but only transformed.

It has to do with the number of possible four-dimensional positions a quantum particle can take between two locations. As your own mathematicians have learned, some infinities are larger than others.

The quest of the absolute leads into the four-dimensional world.

The rhombic dodecahedron is a three-dimensional shadow of the four-dimensional tesseract analogous to the hexagon as a two-dimensional shadow of the cube.

The appearance of a four-dimensional world is due to Minkowski. Einstein showed the relativity of the familiar quantities of physics; Minkowski showed how to recover the absolute by going back to their four-dimensional origin and searching more deeply.

The nature and scope of security threats in the cyber era are four-dimensional compared to the early nuclear age.

Rotating in four-dimensional space unifies the concept of space and time, turning one into the other as the velocity is increased. This beautiful, elegant concept, that symmetry unifies seemingly dissimilar entities into a pleasing, harmonious whole, guided Einstein for the next fifty years.

Moving provides meaning for our humble (if still vicious) life of four-dimensional existence. Four-dimensional existence makes the frightening fox hunt into an entertainment, or war into a pastime or a sport. Even when evil is dull and monotonous, there tends to be a lot of movement, action and entertainment involved. Maybe movies are evil.

How can a four-dimensional and a five-(or ten-)dimensional theory have the same physical implications? What is the analog of an object traveling through the fifth dimension, for example? The answer is that an object moving through the fifth dimension would appear in the dual four-dimensional theory as an object that grows or shrinks.

Salvador Dali's unusual rendering of the crucifixion, "Christus Hypercubus," employs a tesseract to convey a four-dimensional aspect for this unique event.

In short, what Brown, Enquist, and West are saying is that evolution structured our circulatory systems as fractal networks to approximate a "fourth dimension" so as to make our metabolisms more efficient. As West, Brown, and Enquist put it, "Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional … Fractal geometry has literally given life an added dimension.

By framing the special theory of relativity as a four-dimensional theory set in spacetime, Minkowski showed how time dilation and length contraction could be constructed as rotations that transform space into time.