Further reading

Entropy, codes and mutual information explained with pictures. The useful connection is between uncertainty and how much space a message needs.

An early attempt to turn reasoning into systematic calculation. A short route into a surprisingly modern question: which parts of thought can become rules?

Different mathematicians can want very different things from a proof. This looks at the styles and priorities behind those differences.

What do we gain by calling thought a computation? A survey of the idea and the questions it still has to answer.

Representations spread across a network rather than stored in one neat place. An introduction to what that buys you, and what becomes harder to explain.

A defence of ordinary knowledge against philosophical doubt. How much of everyday life should a theory have to preserve?

Rules do not always arrive as instructions. Sometimes they are built into the objects around us, quietly shaping what we do.

Why carrying some direction from the last step can make optimisation faster—and when that same momentum sends it past the target.

Software gets harder to change when too many things depend on one another. A practical look at the boundaries and abstractions that help.

Hearing needs more than a list of frequencies. The trade-off between time and frequency is a useful way into what an auditory representation has to keep.

Using persistent homology to compare leaf shapes. A concrete test of what a topological summary keeps, and what it throws away.

A symmetry-based route into positional encodings: what can group theory tell us about the way attention handles relative position?

A map of transformer variants and the problems they try to solve. Useful for keeping the architectural changes connected to their purpose.

Do mathematical objects exist independently of us? A tour of the case for that view and the objections it has to face.

Organising a large Lean formalisation around a readable proof blueprint. It makes the gap between an explanation and a fully checked proof easier to see.

Being computable and being practical are very different things. Complexity changes what some familiar philosophical thought experiments can assume.

Practical notes on making software faster, with measurement doing the heavy lifting. The question is whether the real workload actually improves.

Forces, steering and balance, with moving diagrams that let you follow the mechanics rather than take them on trust.

Following an engine through its cycle, from pressure in a cylinder to rotation at the output. Timing and geometry make the parts work together.

Trying to pull interpretable features out of a network with dictionary learning. The challenge is telling a convincing label from a useful explanation.

Feature extraction at a larger scale, including the Golden Gate Bridge feature. Changing a feature gives a sharper test than simply naming it.

Informed trading has to reveal information without revealing too much at once. A model of that tension, noise trading and market depth.

Under a particular set of assumptions, new information does not produce speculative trade. The assumptions are where the interesting discussion starts.

Do changes in dividends justify how much stock prices move? The comparison puts pressure on the assumptions behind the dividend-discount model.

Small local preferences can add up to strong sorting. The aggregate pattern need not look much like any one person’s intention.

Better prediction does not remove the work of deciding what an outcome is worth. A model of when it supports judgment and when it makes automation possible.