Nathan's phone was ringing.

"Meyer."

"Nate? Ah...I talked to Karen, so...I wanted to talk to you as well. She told me you are fine, but I..."

"I am fine. I just went to find new places."

"Yeah, I get it. I'd like to do that too. The job can be draining."

"I bet."

"But if you ever want to talk with someone, I can listen. I mean..."

"Good to know. Thanks. I'll talk to Karen once I get back."

"Yeah, that's a better idea."

"It is?"

"I just...I mean, she is much nicer than me, right? Like, if I needed someone to listen to me, I wouldn't open up to you. No sir, never."

"Heh, why so?"

"That icy stare of yours...no, no, it's always best to talk to a lady."

"Hmh...yeah, that's true."

"So, ah...I guess Karen asked this already, but where are you?"

"Somewhere north. I'm trying to find a proper map of the area."

"Found any good sights yet?"

"No...everything looks the same. But I'm heading to a lake; should be a good spot."

"Sounds nice. I'll leave you at it, but, ah...don't be away for too long; Karen is really fond of you."

"Like you?"

"Yes, just like me. Exactly. Bye bye, Nate. Lots of hugs."

"Likewise."

Nathan returned the phone to his pocket. Rain calmed down; sun appeared through the clouds, only to disappear in the next moment. Soon, the rocks surrounding the road turned into a sparse forest. Nathan increased the radio's volume:

"...this measure gives us a fascinating result. As we discussed, we have this non-empty set A, and therefore we have the interior, exterior and edge in respect to A."

"And those three sets are distinct, right?"

"Correct. Now, what happens here, is that the size of the exterior – which we have...right there – is zero. However, the size of the interior – what would that be? As we discussed, the sums of the cubes' volumes are finite, so the size of the interior is finite – it's just some positive number."

"Yeah...so then we have the edge of A."

"And that is where we will be amazed. What is the size of the edge?"

"Heh...aah, I really have no idea."

"Remember that the interior, exterior and edge are distinct. Their union is the entire space, and the size of the entire space is infinite – so it has to be so that the size of the edge is infinite."

"...really? So...yeah, I think I see what you mean."

"Note that the edge of A is very abstract. The size of the exterior is zero, so set A fills the space. On the other hand, the size of the interior – or the volume of A, so to speak – is finite. This means that the edge must be infinitely big in terms of Lebesgue measure. So this set A is something with finite volume and infinite surface area – compare it to a three-dimensional ball, for which both the volume and surface area are finite. The behaviour of A is very counterintuitive."

"Can we...draw the edge of A?"

"I'm not sure if anyone can even imagine its basics – drawing it is quite impossible."

Nathan slowed down as he spotted a small building on his right – it was somewhat ugly and shabby, to say the least. Lower half of its walls was made out of red bricks; upper half was just gray and bleak. Next to the building was a parking space, surrounded by a dark brick wall and some steep hills. The road continued through a wide mouth of a tunnel, with some directional signs hanging above it.

Nathan stopped on the parking lot and looked around. Behind the dark wall, there was a small, calm lake – some distant buildings were standing on its opposite shore. Nathan grabbed the camera, stepped out of the car and walked in front of the wall. He looked down and followed a cloud of mist lingering in the forest below – the sight was truly stunning.

Nathan removed the lens cap and started looking for an optimal angle.