# Quotations on science

These are some of my favorite quotations on science that have inspired my work.

The following people are quoted here: John Backus, Nicolas Bourbaki, Murray Gell-Mann, Robert Harper, F. William Lawvere, Mao Zedong, and John Reynolds.

Everyday human activities such as building a house on a hill by a stream, laying a network of telephone conduits, navigating the solar system, require plans that can work. Planning any such undertaking requires the development of thinking about space. Each development involves many steps of thought and many related geometrical constructions on spaces. Because of the necessary multistep nature of thinking about space, uniquely mathematical measures must be taken to make it reliable. Only explicit principles of thinking (logic) and explicit principles of space (geometry) can guarantee reliability.

Nowadays it is known to be possible, logically speaking, to derive practically the whole of known mathematics from a single source, the Theory of Sets. ... By so doing we do not claim to legislate for all time. It may happen at some future date that mathematicians will agree to use modes of reasoning which cannot be formalized in the language described here; according to some, the recent evolution of axiomatic homology theory would be a sign that this date is not so far. It would then be necessary, if not to change the language completely, at least to enlarge its rules of syntax. But this is for the future to decide.

Many creative computer scientists have retreated from inventing languages to inventing tools for describing them. Unfortunately, they have been largely content to apply their elegant new tools to studying the warts and moles of existing languages. After examining the appalling type structure of conventional languages, using the elegant tools developed by Dana Scott, it is surprising that so many of us remain passively content with that structure instead of energetically searching for new ones.

Type structure is a syntactic discipline for enforcing levels of abstraction.

Where do correct ideas come from? Do they drop from the skies? No. Are they innate in the mind? No. They come from social practice, and from it alone; they come from three kinds of social practice, the struggle for production, the class struggle and scientific experiment. It is man’s social being that determines his thinking.

Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two. If you arrive at an insight that has importance for logic, languages, and categories, then you may feel sure that you have elucidated an essential concept of computation—you have made an enduring scientific discovery. Advances in our understanding of computation may arise from insights gained in many ways (any data is useful and relevant), but their essential truth does not depend on their popularity.

A theory appears beautiful or elegant in my opinion when it’s simple; in other words when it can be expressed very concisely in terms of mathematics that we’ve already learned for some other reason.

Discover the truth through practice, and again through practice verify and develop the truth. Start from perceptual knowledge and actively develop it into rational knowledge; then start from rational knowledge and actively guide revolutionary practice to change both the subjective and the objective world. Practice, knowledge, again practice, and again knowledge. This form repeats itself in endless cycles, and with each cycle the content of practice and knowledge rises to a higher level. Such is the whole of the dialectical-materialist theory of knowledge, and such is the dialectical-materialist theory of the unity of knowing and doing.

The dialectical contrast between presentations of abstract concepts and the abstract concepts themselves, as also the contrast between word problems and groups, polynomial calculations and rings,

etc.can be expressed as an explicit construction of a new adjoint functor out of any given adjoint functor. Since in practice many abstract concepts (and algebras) arise by means other than presentations, it is more accurate to apply the term “theory”, not to the presentations as had become traditional in formalist logic, but rather to the more invariant abstract concepts themselves which serve a pivotal role, both in their connection with the syntax of presentations, as well as with the semantics of representations.