Ideas from Richard Hamming’s 1995 lectures “Learning to learn”

Reference: The Art of Doing Science and Engineering: Learning to Learn” course by Dr. Richard W. Hamming (1915-1998) (1915-1998) for graduate students at the Naval Postgraduate School (NPS) in Monterey, California 1995. http://www.nps.edu/

Sigmoid

A lot of natural processes follow a sigmoid growth: they start small, then they grow exponentially, but then eventually they saturate. It’s not necessarily a sigmoid, but has some similar characteristics.

Every 17 years

Knowledge doubles every 17 years. He does a back of the envelope calculation, being a mathematician he’s very comfortable to use calculus for that. It does not seem outlandish. One issue is that it currently requires more scientists. We’ll hit a saturation point on that. Consequences are that the areas of expertise become more specialized and that things are changed technologically 20 years later, you need to come up with new things.

Early feedback

There is the example of the back of the envelope calculation and later when he talks about an iterative, agile project management that gives you more productivity than blindly following a dead end.

Economic incentives for the development of electronic computers

The 1890s US census, which was by law required every 10 years, was looking to take more than 10 years to process before a new one is due. This lead to the development of punch cards, by Herman Hollerith, where holes in the card indicating say the age or gender could be then used to count. This then eventually led to IBM.

Then the Manhattan project (and other e.g. calculating tables of ballistic trajectories for the US army). Imagine large rooms, factory floor size with rows and rows of, almost always, women doing calculations. Hamming says that you get a multiplication every 20 seconds, for short periods of time you can get more, but it’s not sustainable (e.g. people get tired, then they do mistakes, they need a cup of tea, etc.).

It’s interesting to think about these people, having a job, earnings, and how the electronic computers lost these jobs, and how other jobs were created instead. We’re facing today (2026) the same kind if discourse related to AI, the historical experience says that some jobs will be lost, other jobs will be created.

Centralized computers vs. PCs

Computers used to be centralized, expensive, with options to rent time slots where then utilization factors mattered. AI is currently in a similar early situation where it’s centralized (remote in the cloud), expensive, per-token costs. Things might change.

Productivity

He claims that different people have a wide range of productivity for the same time/effort. He mentions this at the beginning for scientists getting results and later for some programmers being up to 10 times more productive.

# Computer says

An image meme was created in February 2026:

  • A human tells the computer: say “I am alive”
  • Computer responds: I AM ALIVE
  • Human reacts: oh my god

In 1995 Hamming mentions that just because the computer displays,prints,says that it thinks, it’s not necessarily so.

Definition bias

When we ask what is intelligence or thinking, we have a bias, interest, to have such a definition that it does not answer in the negative about ourselves.

Meaning

He describes a situation where his wife mentions that it rains. He wonders why she said that, because he can see that it rains. He then realises that what she means instead is: “I finished my tea, I’m ready to have a conversation”.