The Math of Why You Can't Focus at Work

Introduction

When was the last time you had a good day of work? The kind where you got into flow and stayed there long enough to think deeply about a problem?

Paul Graham wrote about this in 2009: a single meeting can wreck an entire half-day for someone who needs uninterrupted time to build something. Sixteen years later, we’ve added Slack, Teams, always-on video calls, and a culture of instant responsiveness. The problem has gotten worse, with the pandemic turning things to 11 but the conversation stays frustratingly vague. We know focus is dying. We can’t say how bad it is or what would fix it.

In this post, I’ll show you what interruption-driven work looks like when you model it with math. Three simple parameters determine whether your day is productive or a write-off. We’ll simulate hundreds of days and build a map of the entire parameter space so you can see exactly where you are and what happens when you change.

One Day in Detail

Let’s start by drawing what one of those “lost days” actually looks like.

Focus Interruption Recovery Penalty λ = 2 /hr δ = 20 m Focus Interruption Recovery Penalty λ = 2 /hr δ = 20 m 0 h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h Recovery Penalty: 20m (Cannot focus) 20m Recovery Penalty: 30m (Cascaded: 3 interruptions) 30m Recovery Penalty: 20m (Cannot focus) 20m Recovery Penalty: 20m (Cannot focus) 20m Recovery Penalty: 35m (Cascaded: 3 interruptions) 35m Recovery Penalty: 22m (Cascaded: 2 interruptions) 22m Recovery Penalty: 20m (Cannot focus) 20m Recovery Penalty: 50m (Cascaded: 5 interruptions) 50m Recovery Penalty: 20m (Cannot focus) 20m Recovery Penalty: 4m (Cannot focus) Focus Block: 81m 81m Focus Block: 57m 57m Focus Block: 26m 26m Focus Block: 9m Focus Block: 25m 25m Focus Block: 2m Focus Block: 18m 18m Focus Block: 6m Focus Block: 8m Focus Block: 6m 9 am 10 am 11 am 12 pm 13 pm 14 pm 15 pm 16 pm 17 pm Recovery Penalty: 20m (Cannot focus) 20m gap Recovery Penalty: 30m (Cascaded: 3 interruptions) 30m gap Recovery Penalty: 20m (Cannot focus) 20m gap Recovery Penalty: 20m (Cannot focus) 20m gap Recovery Penalty: 35m (Cascaded: 3 interruptions) 35m gap Recovery Penalty: 22m (Cascaded: 2 interruptions) 22m gap Recovery Penalty: 20m (Cannot focus) 20m gap Recovery Penalty: 50m (Cascaded: 5 interruptions) 50m gap Recovery Penalty: 20m (Cannot focus) 20m gap Recovery Penalty: 4m (Cannot focus) 81m 9:00am 10:21am 57m 10:41am 11:38am 26m 25m You managed 3 h 58 m of focus time and 1 deep work blocks (>60 m), though 19 interruptions cost you 242 min of potential productivity, capping your longest uninterrupted stretch at 81 min.

The visualization above shows an 8-hour workday as a timeline. Green segments represent real, uninterrupted focus blocks—the time when you’re genuinely working on the problem. Red lines are interruptions: a Slack DM, a meeting, someone asking a question. The hatched gray zones are recovery time—you’re back at your desk, but you’re not back in the problem yet. The amber and red sections are where you’re partially in the zone—where your focus is broken before 30 or 15 minutes respectively. The goal is to be in the green (or blue).

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