# Normal & counterparts

We are brothers of like paths
order is vital to us.

There is the straightforward one,
always climbing till he's done.

The other two can't stand the heights;
we bunjee jump at middle sites,
to start again with all our mights.

But one of us dropped more,
to see more of hell's floor,
to gain just a bit more lore.

The last ends up where he started,
but isn't visiting the same place...fainthearted?


To me, this appears to describe:

The shapes of four famous graphs: $$y = x$$, $$y = sin(x)$$, $$y = cos(x)$$ and $$y = tan(x)$$.

We are brothers of like paths
order is vital to us.

'We' are graphs, paths whose value (y) depends on another ordered value (x).

There is the straightforward one,
always climbing till he's done.

$$y = x$$
An ever-climbing line:

The other two can't stand the heights;
we bunjee jump at middle sites,
to start again with all our mights.

[Another] two are sin(x) and cos(x), lines which constantly rise and plunge back down through zero, as if bungee jumping.

$$y = sin(x)$$

$$y = cos(x)$$

But one of us dropped more,
to see more of hell's floor,
to gain just a bit more lore.

The last ends up where he started,
but isn't visiting the same place...fainthearted?

If we interpret these two paragraphs together, these could be seen to describe y = tan(x). This one 'dropped more to see more of Hell's floor' since the line goes way past zero into the negative numbers, veering off towards (negative) infinity. In fact, the lines followed by [this] last [brother] start at (negative) infinity and end at (positive) infinity - a bit like ending 'where he started' and yet not 'visiting the same place'.

$$y = tan(x)$$

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• The last one could also be rot13(n pvepyr) – El-Guest Jul 7 '20 at 15:03
• @El-Guest Yes I did consider that, but it seemed to me that really would be 'visiting the same place', so I ended up discounting it... – Stiv Jul 7 '20 at 15:32
• This is very interesting! Not the intended answer though. I'm gonna include a more specific tag. – George Menoutis Jul 8 '20 at 11:21