Talk:Triangular array

Was that a good idea?

@David Eppstein: Er, your edit changed a definition that I thought was helpful precisely because it was more formal than the previous informal one to basically a repetition of the previous sentence. I wanted to use formal mathematical notation like a_ij. (The exact wording I chose has the benefit of being correct whether you're using 1-based or 0-based indexing.)

I'd rather include something more formal like I originally wrote, or just delete the redundant sentence. Since either would do violence to your edit, could we discuss it?

(I was also thinking of describing the standard implementation in computer memory per https://stackoverflow.com/questions/17406593/triangular-array but the inverse mapping is a bit tricky. I.e. given k = i(i+1)/2 + j, how do I re-derive i? It's something messy involving the integer square root.)

38.39.199.2 (talk) 05:03, 30 October 2019 (UTC)

Especially in the lead, but more generally in all Wikipedia articles, formality needs to take a back seat to understandability. It does not make it any more accurate, rigorous, or correct to express the same thing in notation rather than words; it merely makes it harder for the uninitiated to understand. We should be working to make mathematics understandable to all, not building ivory towers of obscurantism to keep others out. See WP:TECHNICAL.

As for your re-derivation of i, that one is messy enough that a formula rather than words probably is the right way to express it. It's

$i=\left\lfloor {\sqrt {2(k+1)}}-{\frac {1}{2}}\right\rfloor .$

But you should probably find a reliable source for an equivalent formula before adding it to the article rather than taking my word for it. —David Eppstein (talk) 05:30, 30 October 2019 (UTC)

@David Eppstein: "It does not make it any more accurate, rigorous, or correct to express the same thing in notation rather than words; it merely makes it harder for the uninitiated to understand." Wow, I'd like to strongly disagree. While some things can be said just as well in words, when things start getting complicated, the ambiguity of natural language often becomes a stumbling block.

When that happens (and it doesn't always happen, but I'm interpreting your words as suggesting that it never happens), the reader needs to "know what is meant" to resolve the ambiguity. That, IMHO, requires even more mathematical background than formal notation. (FWIW, the most common problem I have is running out of pronouns and having to come up with names. It can be unclear if two similar names refer to the same thing or there's supposed to be a distinction. If I use variable names, it's unambiguous.)

You're right that formal notation can be a barrier, which is why I like to say things twice, once each way. Lots of computer-related articles include both a prose description and source (pseudo)code for the same reason.

It can also become ponderous to add all the side conditions in prose. Is the base case i=0 or i=1? Is a theorem true for all primes, or only odd primes? Are negative integers included? Must the triangle be non-degenerate? It's not that such things can't be expressed in prose, but rather that they obscure the explanation. I like to include an informal description which omits such minor details in order to focus on the main idea, and include the details (which are necessary for correctness) in the formal description.

38.39.199.2 (talk) 12:26, 30 October 2019 (UTC)

Such a thing might be helpful later in the article, but technicality is not good for the lead. By the way, I'm not convinced that (row, column) is the simpler way to index these things, at least for infinite triangles (the case mainly considered here). (column,row - column) with zero-based indexing gives a scheme in which the row is easily recovered as the sum of the two coordinates and in which the only condition is that both coordinates are non-negative.