Celebrating our mathematical thinking

Rapunzel, don't sweat the small stuff!

It's a little known fact that the real Rapunzel story was never published. Fragments of it were discovered recently. Here's a quick summary of the rescue scene from the "real" Rapunzel story ...
" ... when the prince climbed up and through the window, he discovered that her cell door was wide open ... "Why didn't you walk out the door?" he asked surprised ... Rapunzel replied: "To get to the door, I first have to first pass half of the distance to the door (1/2 of a metre), then half the remaining distance to the door (1/4 of a metre), then half of the remaining distance (1/8 of a metre), and so on an on and on." ... "Oh, don't be silly" said the prince, as he kissed her, which caused Rapunzel to take her mind off of all the fractions, and she and the prince dashed out the cell door ... "Hmm," she thought to herself later that day ... "I can walk through the door if I don't think about all the distances I have to travel to get there. But I can't if I do think about them."

Rapunzel, Rapunzel
Your tower door is open
But you just can’t imagine
Walking half way to freedom
Then half of what’s left
And half of what remains
And so on and on

Rapunzel, Rapunzel
You have concluded
That you can’t get to the door
As the fractions go on and on
And so would your steps
watch them go on and on

Distraction, is the key, and
Sometimes you need
To “let down your hair”
Relax and move forward
Don’t sweat the small stuff
Because there is no
obstacle in your way
Don’t sweat the small stuff

My brain hurts when I ask this
Says Rapunzel in reply
But does taking
Increasingly smaller steps
Cause me to eventually
Be walking backwards?

But then I realize,
That we are ALWAYS
Crossing these distances
And we still arrive
At all kinds of destinations
I’m crossing fractions of a distance
All the time

Reminds me of all the stuff
I have to do
And continually thinking about it
Slows down my ability to get it done
Or doing laundry
Once you've finished all your loads
Another dirty shirt gets thrown in the basket
That is truly infinity
Have I switched from math
To philosophy?

Then Rapunzel smiles and winks
I love how fairytales
Can be subtly subverted

Rapunzel, Rapunzel
Your tower door is open
To offer new insights
Fresh ways of looking at math