Walked along the canal, coffee in hand, thinking about pace. The city moves differently here — slower, more deliberate. Every corner has a story, every alley a hidden shrine.

afternoon

Bookstore stop, notes in the margin, no rush. Found a first edition of a math book I’d been hunting for years. The owner wrapped it in brown paper like it was something precious.

snapshots

• tiny kissaten near the station
• the sound of bikes on wet pavement
• late light on old wood
• a cat sleeping on a temple step

reflection

Sometimes the best days are the ones with no agenda. Just walking, watching, being present.

When analyzing stream ciphers, we often need to understand the relationship between bias and correlation. Here’s the key insight I always have to re-derive.

the statement

For random variables $X$ and $Y$ over ${0,1}$:

where $\varepsilon$ is the correlation bias.

why it matters

This simple relationship is the foundation of differential-linear cryptanalysis. The bias propagates through rounds, and understanding how it compounds is key to breaking ciphers.

The key insight is that for independent biases $\varepsilon_1, \varepsilon_2$:

quick notes

• Bias compounds multiplicatively (mostly)
• Independence assumptions matter more than we think
• Always check your experimental correlations against theory

It’s harder than it sounds — waking up early, not checking the phone, sitting with a notebook and a problem.

what works

• No screens for the first hour
• One focused task, nothing else
• Coffee helps (obviously)

what doesn’t

• Trying to do this every day (burnout is real)
• Being rigid about the routine
• Feeling guilty when it doesn’t happen

the point

Slow mornings aren’t about productivity. They’re about having space to think. Sometimes the best ideas come when you’re not trying.