# Very basic question: what is an accepted term for “linear order distance”

In data science we have "Manhattan Distance" as a slang term for Level 1 Distance and "Euclidean Distance" as a slang term for Level 2 Distance. Is there an accepted term for linear distance in memory of cells in different rows in a matrix? That is, given an 8x8 matrix, the "linear distance" from [3,2] to [4,5] is: (4-3) * 8 + (5-2)

This is the distance in memory addressing. "Level 0 Distance" doesn't really work as a technical term, because computer memory layout is not a native concept in mathematics. Is there a standard term for this? It reminds me of the old flyback transformers in cathode ray tubes, so "flyback distance" makes sense as a slang term.

• This doesn't strike me as common enough to have a standard name, though I've also never heard "Level i Distance" before, so maybe I'm just coming from the wrong field. I'd suggest also "reading distance" as being evocative of the meaning. – Ben Reiniger Jan 29 '20 at 0:07

## 1 Answer

Actually this is the Manhattan / $$L_1$$ / Norm 1 distance, if you just multiply the row by $$8$$ (or $$N$$).

The $$L_1$$ distance between $$[24, 2]$$ and $$[32, 5]$$ is what you are looking for.

• Right, it's the L1 distance of the matrix linearized. But that linearization is not a mathematical concept, it is just an implementation detail. I'm searching for some reason to not just fabricate my own word, "flyback", for this distance. – Jack Parsons Dec 30 '19 at 23:25
• I think this is different: AIUI, the OP's distance from [3,5] to [4,2] is 5, not 11. – Ben Reiniger Jan 29 '20 at 0:02