Work in the invisible world at least as hard as you do in the visible one” ~ Mawlana Jalaladdin Rumi

What if the “invisible” were around you, and you could not see it, … unless you worked hard, really hard. And even if you worked really hard, the only thing you could saw was his shadow. The invisible’s shadow visible. No, by all means, my post is not about religion, believe me. Instead, valid science. For instance, if I gave you 6 matchsticks, and ask you to draw 4 triangles without crossing any two matchsticks, could you do it? The answer is positive. If you really think out of the box, indeed you can.

Carl Sagan (below) starts with a famous passage from Edwin Abbott Abbott‘s “Flatland – A Romance of many dimensions” (which I do vividly recommend – book cover above). A spheric creature from the 3th dimension visits Flatland, where only 2th dimension creatures live. And while a 2-D (a square) creature keeps worrying about his own sanity, the 3rd dimension creature feels highly frustrated with the outcome from their Spielberg-like “Close Encounters of the Third Kind“. In fact, the sphere his unhappy for being considered an psychological aberration.  At his own risk, and without worrying about his hypothetical unfriendly gesture from dimension to dimension, the sphere then, decides to start some ‘bizarre‘ experiences. The story goes…, but suddenly, Carl do moves on, … on what really matters:

[…] Getting into another dimension, provides an instantial benefit, a kind of X-ray vision […] Well, (says the square), … I was on another mystical dimension, called ‘Up‘ […] Now, if you look at the shadow, what you see is that not all lines appear equal, not all the angles are right angles […] The 3-D object has not been perfectly represented in his projection in 2 dimensions, but that is part of the cost of loosing a dimension in the projection […]  Now, I can not show you a tesseract , because I and you are trapped in 3 dimensions, but what I can show you is the shadow into 3 dimensions […] The 4-D hypercube, the real tesseract would have all right angles. That’s not what we see here, but that’s the penalty of projection […]

[…] So you see. While we cannot imagine the world of four dimensions, we can certainly think about it perfectly well […]