# Pathfinder Alignment Steps Clarification (N/S/E/W without Diagonals)

I have a very quick question about alignment steps in Pathfinder with regard to Clerics/Inquisitors/etc. Using the typical 3x3 chart, alignment steps for character vs deity are measured without diagonal lines, right? In other words, if the chart were a map, each step is N/S/E/W but never NW/SW/NE/SE.

To show this visually:

• These directions are 1 step: ← ↑ → ↓
• These directions are 2: ↖ ↗ ↘ ↙

A NN character is 1 step away from LN, NG, NE, CN. 2 steps away from LG, LE, CG and CE.

A NG character is 1 step away from LG, NN, CG. 2 steps away from LN, NE, CN. 3 steps away from LE and CE.

Is that correct?

Or am I mistaken and ↖ ↗ ↘ ↙ are also 1 step away? So a NG character is 1 step away from LG, NN, CG, LN and CN. 2 steps away from LE and CE.

• Excellently formatted first question, and welcome to the site! When you get a minute, check out the tour and help center and you'll get a badge. Hope to see you around. – Please stop being evil Oct 4 '17 at 7:39
• I prefer to think of it as diagonal steps being illegal, and then just count the number of N/S/E/W steps (Manhattan distance). Actually, I personally think of it as the number of letter changes (making sure to go thru neutrals as required) but I suspect that's just an artifact of how my brain works and isn't helpful to anyone else... CE -> CN -> NN -> LN -> LG = 4 – A C Oct 5 '17 at 3:16
• This could make for a funny Code Golf question. – Nat Oct 5 '17 at 7:50

## You are right.

The steps mentioned are straight orthogonal ones, so for a diagonal you need two of them. For example a Cleric of Norgorber (NE) can be either LE, NE, CE or N, but no other alignment.

• I am basically saying the same thing as @TheVagrantDog, but his answer provides many details where I just wanted to provide an essential answer. – Anne Aunyme Oct 4 '17 at 8:08
• Essentially the point of this rule is so that you and your god agree on something. A LN character and a NE diety aren't going to find any common ground about how to deal with any given situation, hence why the character has to be one step in an orthogonal sense. – Draco18s no longer trusts SE Oct 4 '17 at 14:39
• @Draco18s: I never thought about it that way before, but it definitely makes sense. – Anne Aunyme Oct 4 '17 at 15:22

It's a little difficult to read the number of steps on a 3 x 3 chart, because when we talk about steps we're discussing a pair of axes, not a set of squares. Still, it can be done. Typically, when you're looking at the steps chart, you figure on 1 step in a normal direction, 2 steps for a diagonal. Here's a different way to look at it though, if that helps.

Pretend the 3 x 3 chart sits on an x-y graph, with the good alignments at 0 on the x-axis and the chaotic alignments at 0 on the y-axis. It'd look something like this (forgive the paint job):

Every alignment has a set of coordinates to go with it. Chaotic Good would be (0,0), Lawful Evil would be (2,2). Want to know the number of steps between two alignments? It's the combined difference between each of their x and y coordinates. Chaotic Good is {(2-0)+(2-0)} 4 steps from Lawful Evil. Neutral Good is {(2-0)+(1-0)} 3 steps from Chaotic Evil. So on and so forth.

Either way should work for you, but hopefully you'll be able to understand it better with the visual right there.

• You didn't put true neutral at (0,0)? Shame. The end result of the math works the same, but the graph and intermediate math is so much better. LG becomes (+1,+1), CE becomes (-1, -1), TN (0,0). – Yakk Oct 4 '17 at 15:11
• I tried to avoid negative numbers for those not mathematically inclined. – TheVagrantDog Oct 4 '17 at 15:36
• Very well, next time I'll suggest Z[i] – Yakk Oct 4 '17 at 16:08
• For those who are mathematically inclined, this method of measuring distances between squares is known as the taxicab metric. – jwodder Oct 4 '17 at 16:48
• Ooh, good catch. I am impressed you noticed. – TheVagrantDog Oct 4 '17 at 16:50

Another way to look at alignment steps is with a chess-oriented brain. If a rook can travel from one alignment to another by hopping one space ahead, it's one alignment step. If a Bishop can travel to the alignment you'd like, it's 2 steps.

I hope that kind of makes sense!

• That's a strange way to look at it, but I do think I get the gist of what you're saying. – Kot Carson Oct 4 '17 at 11:05

The alignments in Pathfinder can be treated as points on Z[i].

    -1      0      1
i   LE      LN     LG
0   NE      N      NG
-i  CE      CN     CG


To find the distnace between alignments, first subtract

LG - CN
(1+i) - (0-i)
1+2i


Now take its magnitude, add 24%, and round to the nearest integer.

sqrt(1+4)*1.24
=~ 2.77
= 3 after rounding


you'll find this gives the correct result in all cases.

The effects of multipling alignments together is left as an exercise.

• +1 for humor. Just to note it, the mathematical description would be that alignment steps are the $L^1$-norm in $R^2$. – Nat Oct 5 '17 at 7:44
• I'd really like to know where the 24% came from here – Ev- Nov 9 '17 at 19:45
• @Ev- Well, 25% is too much, and 23% is too little. – Yakk Nov 9 '17 at 20:14