If you've seen the movie Interstellar (2014), and I recommend that you do, you may have heard the word tesseract used to describe the manifestation of time as a physical dimension and seen it's magnificent portrayal inside the black hole Gargantua. The Marvel version is a bit more cryptic - a source of great power and key to travelling to and from Asgard in the Avengers movie (ah, Loki, when will you learn: Hollywood loves an ending where good triumphs).
In geometry, the tesseract is the four dimensional analog of the cube. Or to put it another way, a tesseract is to the cube, what the cube is to the square. So while the surface of the cube is made up of six square faces, the hypersurface of the of the tesseract is made up of eight cube faces. But wait. A cube face? What does this mean? Well please feel free to spend a lazy afternoon trying to imagine it. But let me warn you it is a four dimensional construct, and if you're like me, the regular three dimensions plus time are baffling enough.
If you've got some wire and some detergent though, you can have a mathematically rewarding play for a half hour. Bend some wire to make a cube - neat as you can but you're not being judged on this so keep it real. Just make sure the corners touch for later, when you dip it in the detergent.
Got your cube? Hold it in the sun. Play with the shadows? Can you make a square? The three dimensional cube casts a shadow on a two dimensional plane that is it's two dimensional analog. Interesting. Now dip your wire cube into soapy water, as if you're about to blow bubbles. Look at the iridescent angular planes and the smaller cube inside. This is the shadow a tesseract casts on the three dimensional plane we think of as our reality. A three dimensional picture of the shape you will never see.
What other shadows are there of things that you cannot see. Your partner's dark secrets, manifested in the idiosyncrasies of their repeat offences and curious behaviours. The boss who sings your praises while all the time undermining you with an unseen agenda, setting you up to fail. The fairweather friend, who spends his summers out and about but suddenly calls when the skies turn dark.
Look deeply into the shadows. Measure them, taxonomically. Map them. Delineate their projections across all your dimensions. And then turn your gaze upward. Towards the light. Do not play with the shadow - it is merely an analog. Go for the real thing. Look directly into the light and see things for what they really are.
Better still look at your own shadow. Do you really know the full shape that casts it. The unseen shape. Turn towards your own light and understand all of your dimensions. Perhaps this is enlightenment.
