Context switching is, in the literature, known to be productivity destroying, and while it may feel like a very productive day if I do things from four categories, I can tell you that when I actually go back and look at the results it is feelings-nothing-more-than-feelings.
e.g. If I were doing nothing but customer contact mode, I know that I can send 50 emails in a day of moderate complexity. (e.g. Consulting mini-proposal for a client, support issue for BCC customer, pre-sales question for AR, ... x50. I know this because I have verifiably done it on e.g. launch days before.)
I did four things today -- video recording, hopped on a call, sent emails, and... shoot, only three things but I thought I remembered four. My subjective experience is that 1/3rd of my day was email. How many emails did I send? 1/3 * 50 = ~15? No. Five. And it (subjectively) felt like pulling teeth even though three of those were the same email with a few hand-written edits in the middle of them, whereas after I get into email flow mode for I can normally do two hours without getting bored.
I've got at least two hours into working with video today. How many 5 minute videos have I completed? Umm, zero.
Contrast this with yesterday: yesterday I putzed around to 6 PM and then coded until 10 PM then quit for dinner. I got two features coded and tested then squashed a pair of bugs. Yesterday feels non-productive in some ineffable way ("I putzed around until 6 PM! I only worked 4 hours and my salaryman brain rebels against the sheer laxity! All I did was code six measly little commits!") but it almost certainly added more to the business.