User john ruskin - MathOverflow

Space/Time Transform in solving N vs NP

2010-08-18T12:23:48Z

Let me try this again, as an engineer that I am, and not as a theoretical mathematician.

Often, in engineering, in complex engineering, the solution path to evaluating a question requires an analysis that removes dimensions from the question. Examples include analysis of air flow around and against an an air foil; mass transport [or heat] with some given initial conditions. Variations of those solution paths include using transforms, or dimensionless variables [for example, like the Reynolds number in wing design...]

As I see it, and perhaps this is the preliminary question...., P vs NP asks if something can be accomplished given enough time, given that there are solution 'spaces' [ie, solution paths] along which a forensic mathematician might move, one or more of which may end up with a solution.

So, in this context, I ask this, again: Why doesn't the analysis of the question, P vs NP, deserve a look which undertakes a transform that removes time as a variable. Or, alternatively or in the conjunctive, transforms the space.

Answer by John Ruskin for Should one use "above" and "below" in mathematical writing?

2010-08-18T12:42:52Z

Practically, numbering equations works, sequenced in the article from beginning to end. While it is a courtesy to readers and arbiters, later, who discuss lines that the author did not, it most certainly adds specificity, without tortuous sentence structure or word choice. "Equation 24" will always be just that, regardless of its placement on the page, and regardless of reprint formulation or quality.

As an editor, my choice is to number all equations, and bold those that are referred to by the text of the article.

Equation identification, when there is textual sectioning, by chapter or other means, can include the section as predicate: e.g.: 5-24 refers to equation 24 in chapter 5. Texts that use this system (or any system) wisely place an explanation at the forward.

Obviously, longer papers/articles, or complex sectioning, both complicate the system for the reader, the ultimate consumer for the publication (e.g.: 5.3-24). Personally I would avoid it; I can't imagine the necessity of referring to large counts of equations in other chapters or sections, and in those rare cases, for a reference such as "see equation 5-24", I would consider adding a postscript: "in Chapter 5.3" or "at page 137".

Comment by John Ruskin

2010-08-18T13:17:17Z

I distinguish, in my mind, between, solving without using the concept of time, to undertaking an actual transform.