Today, we’re matching the power of dreaming with the energy of intention, so that we can catch our dreams and turn our wildest fantasies into our reality. It’s in our dreams that we plant the seeds of our future. I don't know if this helps imagining 4D geometrical objects in general, but for the 4-sphere defined by R 2 = x_1 2 + x_2 2 + x_3 2 + x_4 2 centered at (0,0,0,0) it would look like a solid sphere where the color increases (more white) in towards the center because the x_4 value must increase as the 3D coordinates decrease.Dreams are not a childish waste of time. In this way you can imagine 4 dimensions: 3D space where each point also has a color. You can map the interval to (-Infinity,Infinity), so it's legitimate to associate a single color to a single value of x_4. Say you define the color quantity that ranges from 0 (black) to 1 (white). The insight is that you can attach something intuitive to that degree of freedom, like color or opacity. In this way we see that 4-D space is like 3-D space where each point has one additional degree of freedom that can range from -Infinity to Infinity. One technique that I heard or read about at some point is to consider that a point in 4 spatial dimensions is indexed by 4 numbers (x_1, x_2, x_3, x_4). We make our world significant by the courage of our questions and by the depth of our answers. For more open-ended questions, try /r/AskScienceDiscussion | Sign up to be a panelist!.Looking for flair? Sign up to be a panelist!.
#IMAGINING 4D OBJECTS SOFTWARE#
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