It is unclear whether one is ever using a 'method' at all, because thoughts constantly arise in the mind and it is a stretch to attribute all such thoughts to a method rather than to their simply arising.

Excessive identification with 'science' and the question of whether one is 'really a scientist' has a counterproductive effect on what people actually do, because it makes them wonder what they should do in their capacity as scientists rather than just pursue the problem.

The Popper-Miller theorem (Nature, 1983) argues that the probabilistic support a piece of evidence confers on a theory cannot be understood as the evidence conferring inductive support, because by splitting a theory relative to the evidence into a deductive part and an inductive part, the evidence always decreases the probability of the inductive part.

While certain patterns of thought seem more conducive to understanding nature than others, which patterns work and how to think about them remains more of a great mystery than an exact science.

The most important thing for a young person seeking to contribute is to connect with other people or groups already doing something, where they will find something to contribute to and gain support; there is no such thing as an objectively 'unsolved problem' list, because value is only to a subsection of people who may not know in advance what they want.

What people actually want and believe in are not contentless-but-likely tautology-like theories, but highly informative, explanatory, and therefore less probable theories—Popper became skeptical of probabilistic approaches to knowledge for this reason.

Becoming self-consciously aware of and classifying what one is doing can be counterproductive, paralleling the phenomenon of self-consciousness known to cause problems in many other domains.

The constraints obeyed by a measure of a theory's logical content are exactly the same as the probability calculus, so a probability assignment can always be consistently reinterpreted as a statement of a theory's degree of logical weakness—saying one theory is more probable than another can mean it says less.

The activity of understanding the natural world works better when institutionally and culturally supported—keeping relevant books and people in one place and organizing events—so universities are worth supporting even if the unified concept of 'science' is not the right way to understand the activity.

The activity of understanding nature need not be conceived as unified: like entrepreneurs building different companies without anyone asking whether each is 'really entrepreneuring', researchers each pursuing distinct topics (liquid helium, star swarm evolution) can be institutionally supported without classifying them all as doing one thing called 'science'.

The term 'scientist' is an early 19th-century invention traced to two professors at Trinity College, Cambridge, yet people were able to do science well before that, showing the identity is not necessary to the activity.

One can reach a better understanding of the natural world without ever becoming conscious that one is doing anything special, since people have always investigated nature without a special social role for it.

The idea that there is a specific scientific method that one ought to use—rather than following where the logic of the problem itself leads—can stop people from doing sensible things that would help them pursue their problem.

Karl Popper, despite being a professor of scientific method at the LSE, said the subject he professed does not exist, and Feyerabend wrote a book 'against method', so prominent philosophers of science dispute that a privileged scientific method exists.

Hume's problem of induction shows there is no way to proceed logically (by reason) from experience to the celebrated general theories of the Enlightenment such as Newton's, undercutting the Enlightenment idea that reason was the route to understanding nature.

The narrative attributing the Enlightenment's success to a change in method may itself be a fiction; alternative explanations such as economic progress enabling more thought are difficult to rule out, and figuring out causality in such historical matters is very hard.

The conjunction fallacy—shown in Kahneman's Linda experiment where people judge 'banker and feminist' more likely than 'banker' alone—demonstrates that people seek explanatory theories that fit the given information rather than the most probable option.

The Popper-Miller result poses an interesting challenge to using Bayesian reasoning to build an AGI or for related purposes, because it questions whether probabilistic updating captures inductive support.

In German and Slovenian the word for probability translates roughly as 'believability', and the believability of explanatory theories is always higher than that of less likely theories—so believability isn't really probability.

Becoming a polymath is not something you learn to be but something you unlearn to be: people are naturally interested in everything, and self-conscious, systematic attempts to learn—studying 'fundamentals, then intermediate, then advanced' levels—are misconceptions that lead in counterproductive directions.