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A compelling if painful story. You must have some thoughts about what you could have done to track down the spreadsheet problem sooner – what are they? Also, if you could change Excel in any way you chose, what might be ways for it to prevent or detect such problems?

I'd like to ask about a technicality as well, if you don't mind. You said that ROUNDUP was used in hundreds of formulas and ROUND in only one. How many of these formulas were identical except for relative cell references, as opposed to doing logically distinct things? By "identical except for relative cell references" I mean the kind of formulas you get by selecting a cell and telling Excel to copy its formula across a range -- Excel sees these as distinct formulas, but really they're computing the same thing on different inputs; in APL it would be a single expression. I'm wondering if the bad ROUND guy was identical to some other formula in the sheet, or whether it was a fundamentally new formula that someone typed in and forgot to use ROUNDUP. Really, I guess I'm just wondering how the bad formula happened to get entered.

The reason for that last question is that I'm interested in what a spreadsheet would be like that recognized common formulas across a range and treated them as a single data-parallel computation, rather than a bunch of separate cells that happen to have relatively identical formulas. Clearly this would have performance advantages (parallelism and data locality). But it would also seem to have a better chance at preventing errors, since it would treat "computation X across an array of N cells" as a single thing, rather than N relative copies of X that might get altered separately. Curious to hear your thoughts on that general idea too.




Not many people on HN mention APL. I programmed in APL professionally for almost ten years and know (knew?) the language well.

It's too late for me to go dig-up this old spreadsheet. Maybe I'll do it tomorrow. Excel does warn you when there are discrepancies between adjoining cells. If I remember correctly this was a cell that was copied down and used on a row. Thinking back I think the formula was entered once but replicated Dow a range of rows.

The problem with the APL comparison is that the language can become less elegant if the operations to be applied across the rows of a matrix are somewhat varied. I'm typing on an iPad right now so I can't even try to give you an APL example. Maybe tomorrow from my PC.


(I remembered your APL experience from some previous HN comment or other.) You're right that spreadsheets tend to be more heterogeneous than a chain of array operators. I'm not suggesting that APL as a language should be integrated into spreadsheets, but rather that there is a way to implement spreadsheet language (formulas and cells) that partially approaches how APL treats computation. This is possible because there is a lot of implicitly array-oriented computation in typical spreadsheets – that's what you're "declaring" when you drag a formula across a range of cells. What would a spreadsheet system be like if it really exploited this? The trick is to do it without breaking too much with the well-established mental model of Excel users.


Excel does have array formulas. Every time I used them I have to look up usage. From memory they work well for matrix transforms and such things. Again, my memory fails me because It's probably been five or more years since I've touched them.

I have a busy day today so I have to stay off HN. I'll look into some of the items requiring deeper answers later tonight or tomorrow.


"Excel sees these as distinct formulas, but really they're computing the same thing on different inputs; in APL it would be a single expression."

Excel notices when there is one formula that breaks a pattern, and puts a warning sign on that call (my Office 2003 version of Excel does). Now it presumably misses some cases, but the standard 'drag a formula, change one of them' case, Excel saves you from.




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