Order-of-magnitude Calculation, Or: How Many Numbers Am I Keeping Track Of?

I haven't talked about it much on here, but I'm coming to the end of my original three-year PhD period at the end of September, a week prior to which I've got my final annual review. I'll be applying for a six-month extension to finish writing the two papers which will contain the majority of my original contributions to the sum total of human knowledge, and which will make up the bulk of my thesis. I'm currently in the process of trying to get some results from all the measurements I've spent the past almost-three-years collecting, correcting, collating, and calibrating.

I got to thinking on Friday about just how many numbers I actually have to keep track of. I'm just going to do a quick order-of magnitude estimate here, as it'll get us close enough that it won't really matter. For starters, I have around 11,000 different observations (divvied up between 144 stars, but that's not really relevant here). In each observation, I've attempted to make ~150 measurements of the wavelength of specific absorption features corresponding to particular atomic transitions. Now, these ~150 measurements get several corrections applied to them, and I keep all those corrections and corrected measurements around too so I can go back and check them. This adds up to a total of 9 different arrays.

From those ~150 transition measurements I also construct ~200 pairs of transitions and collect measurements for them (which are the real results of my research), and that comprises (currently) another 3 arrays. There are a few more numbers I keep track of per-observation, but few enough that I'll leave them out for now. Doing the math here:

\[11000\,\text{observations}\times9\times150\times3\times200=8.91\,\textbf{billion}\]

Yes, that's “billion” with a b. I'm actually surprised by this, because when I first tried doing this on Friday I got an answer an order-of-magnitude lower (22.5 million). I've done the math here several times, however, and it all checks out. Huh. That's…a lot of numbers. Well, technically, a lot of those are not numbers; specifically, they're Not-A-Numbers, or NaNs—essentially a computer-understandable way of saying N/A for cases were a measurement does not exist for some reason or another. Perhaps it would be better to call them “data points,” as I still need to keep track of which data points are numbers and which aren't, so it's still important for me to have ways to organize and keep tabs on all of them.

That's all for tonight, I just wanted to get that out of my head and down somewhere. Perhaps in a few months when I'm quite certain I won't be adding more arrays of numbers—I added several just this past week, actually—I'll do a more careful calculation and get an exact number, but for now, a hui hou!

Edit (September 8, 202): Argh, I knew there must be a mistake somewhere! I multiplied when I should've added and didn't parenthesize well; the correct calculation should've been:

\[11000\,\text{observations}\times(9\times150+3\times200)=21.45\,\textbf{million}\]

I'm still planning to revisit this and do a post with a more accurate number a bit later on, so keep an eye out for that one.