how to make a klein bottle

start with a square, gluing together corresponding colored edges, so that the arrows match. glue the red arrows of the square together,resulting in a cylinder. glue the ends together so that the arrows on the circles match (pass one end through the side of the cylinder). gradually push a piece of the tube containing the intersection out of the original 3D space. this immersion is useful for visualizing many properties of the Klein bottle. for example, the Klein bottle has no boundary, where the surface stops abruptly, and it is non-orientable (with no distinction between the "inside" and "outside"), as reflected in the one-sidedness of the immersion.

-from wikipedia

uhmm. i can pretty much imagine you scratching your heads after reading the previous paragraphs, hehe. don’t worry. this is *not* about math and topology - er, not entirely, at least, hehe ü

the Klein bottle is a weird surface (for math lovers: it’s very much related to another weird surface, the möebius strip). what makes it odd is that it is a “non-orientable” surface - it has no inside nor outside. what’s even weirder is that the Klein bottle does not exist in 3 dimensions. it is possible to make a 3D model of it.. but one can only view it properly in 4 dimensions.

it’s funny how the human mind can imagine something so complex and so interesting (at least, to me.. and to other math geeks haha) as the Klein bottle. i mean.. technically, it doesn’t even exist! it resides only in the imagination. and yet mathematicians talk about its properties.. its uses (yes, it *does* have practical applications!).. its beauty (yeah, we do find it beautiful, ok?!).

the brain truly is powerful. it can come up with the weirdest, most complicated things. stuff dreams are made of. it can create objects that have not yet been made. it can create objects that can never exist. yup, the human mind sure is great.

we may be blessed with great minds that understand how to make Klein bottles. we may have brains that can solve complex math equations, write inspiring compositions and handle a multitude of tasks. but no matter how superb our brains may be, we can *never* fully understand the greatness of our Lord.

ecclesiastes 3:11-12 says, “He has also set eternity in the hearts of men; yet they cannot fathom what God has done from beginning to end.” we have eternity in our hearts.. yet even that is not enough to contain God’s greatness! how awesome is that?!

we don’t need big brains to know our God, after all. so even if we can’t solve those math equations, that’s all right ü all we need are big hearts - willing to open up to let Him in. He knows us inside out - we’re kinda like the Klein bottle to Him - He sees our inside and outside at the same time ü and He wants to make Himself known to us.

now *that* is reason to be glad, indeed ü