# Standing in a field. What is my name?

I was standing in a field reading a map

and doing something characteristic of me

I felt the urge to take a power nap

but first I needed to go for a pee

• Great riddle! Now I want to add a certain tag to the question, but obviously that would be too big a spoiler ;-) Apr 17, 2017 at 1:10

Oh, of course ...

It's a mathematical riddle. I should have realised sooner.

I was standing in a field reading a map

A field, as in the mathematical object: a set with two binary operations. A map, as in a function acting on elements of this field.

and doing something characteristic of me

The characteristic of a field, in the ring-theoretic sense - the characteristic of any field is always either zero or a positive prime number.

I felt the urge to take a power nap

A power, as in taking powers of elements. The "power nap" here probably means a power map.

but first I needed to go for a pee

A pee, meaning a prime number $p$, the characteristic of the field.

So taking all in all, you are

a Frobenius endomorphism: the map sending any element of a field of characteristic $p$ to its $p$th power.

Feedback section

When I saw Silenus's answer, I thought that was it and the riddle was solved. But then I noticed the bounty and realised that this wasn't done and dusted yet. The second line was what really did it for me: that unusual word "characteristic" must have been chosen for a reason, so why? Then I thought of what might be standing in a field (for a while I wondered if the solution might be "scarecrow"), and why a field specifically. Eventually it clicked that "field" doesn't mean what you'd first think it does, and everything else just snowballed from there. Exactly as it should with a well-constructed riddle: it seems inscrutable at first, but once you get a hold on it, the solution is self-confirming. My only criticism would be that it took a while for me to get the final solution even after I'd realised what the riddle is all about, but we can put that down to the fact that it's been a few years since I've studied any

algebra.

• @Improve and other puzzle setters - "I thought that was it and the riddle was solved. But then I noticed the bounty and realised that this wasn't done and dusted yet" - just a note that if you don't comment on a wrong answer, people may not know if you've seen it but it's wrong, or if you just haven't seen it. A note on incorrect answers is generally a good idea.
– Rubio
Apr 17, 2017 at 2:05

You are a

storm cloud, perhaps.

I was standing in a field reading a map

A cloud might stand high above a field and look down upon the earth, which resembles a map.

and doing something characteristic of me

This action of hovering above earth is characteristic of clouds.

I felt the urge to take a power nap

"Power nap" may refer to lightning.

but first I needed to go for a pee

The cloud needed to produce rain, since moisture is essential for thunderstorms.