PATH HOMOTOPY AND YOUR LOUSY THINKING

A to B be any stretch of your sad, sad existence. Could be the crappy day you just had and can’t sleep away now at 4 am in the morning, the horrible week with the whole world huddling together to knock you down to the ground every step you take, or in fact the whole stretch of your mediocre existence in a world that is so personally hostile and unfair to you. Then you look around and see everyone else living the perfect life you’ll never have. The internet is bloated with them, you daren’t even open Instagram cuz even if it’s the seventh time today you know there are more of them, and outside they’re everywhere: in cafes, parks, buses.

The situation you’re in is smack-on portrayed by Figure A. Everyone else lives their lives riding that blue line while that red line is specially made for you. Behold it and realise how cursed and fucked up you are and that there’s nothing short of a reincarnation that can promote you to a better life.

Now, figure B.

Oh, he’s drawn a few more lines in this one. What wisdom lies here?

Cue jargon:

 

A path homotopy in X is a family of paths 

f_t : [0,1] → X indexed by I=[0,1] such that

·         f_t(0)= A and f_t(1)=B are fixed.

·         The map F:[0,1]x[0,1]→X given by F(s,t) = f_t(s) is continuous.

Enjoyed looking at the mathematics, thanks. Now draw a curve a bit farther down in Figure A for me and let me continue indulging in my self-loathing…

We got two lines f₀(s) and f₁(s) which are fixed between points A and B. And then there are a continuous array of lines in between them. This family of paths is called a path homotopy.

The perfect life is f₀(s) and the shit life is f₁(s). But actual life that happens to all of us every day belongs to the path homotopy, all those lines in between these two idealised versions.

 

Don't dare assume that the prophet is dishing out math statements to make peace with the fact that he's run away from hardcore science and this is his way of making amends... that's heresy cause it ain't true... At least not all the way true damn it. 

Point is, your sad victimised existence epitomised by Figure A is an unrealistic one. Your friends who’re getting together and posting new photos every night might have shit of their own to deal with at times, you can’t judge them to have flawless lives just from their IG posts, c’mon. So with the celebrity model, the singer all the girls are talking about, that football prodigy who’s 18 and killing it (what the hell was I doing at 18?). You don’t actually know what’s going on in their lives, you could give the benefit of the doubt to the possibility that they ain’t living perfect lives. They ain’t on that blue line.

And surely the cleaning staff aunty who hasn’t gone home to see her kids in two months might be suffering a tad bit more than you, you with your all-consuming gloom cuz the presentation sucked. No? How about that person nearby whose kid died recently? Hmm… maybe. So slowly admit to yourself that he might be closer to the red line than you are. Take your time, look around and start filling up the spaces below and above you. You’ll see that there’s always worse-off people than the one you’re looking at, everyone’s likely to have sad shit. And they’re walking around with smiles plastered on their faces and walking around just like you are. Some of them are so good at it they could pass for the upper half of figure B. And the overachieving dickhead friend who’s got that job that’s super fun and pays a lot, hit the ceiling of happiness and nothing seems to go wrong with him, he’s got pains too. Slowly ingrain this into your brain. Difficult in practice, but it’s the likely truth.

f(0) of pure bliss and f(1) of utter despair are idealistic and unreal, we’re all dancing around in between them, billions of us. Tides change and we shoot up and down. But always consider, there’s people worse off and more in dire need of compassion now, and although you’re not currently part of the crowd that’s getting a thousand likes on that photo in which they’re all so freaking happy and vibing and living real, you’ll have your moments too, it ain’t as bad as you think. Remember path homotopy.