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Follow the Bouncing Ball: An Over-Literal Interpretation of 'Mechanized Logic'

Developing your own intuitions is an underappreciated but absolutely essential part of understanding mathematics, computing, or science. In general, more concrete intuitions are also more useful intuitions, as the human mind has a better-developed set of tools for reasoning about familiar objects. 2,325 more words

Interesting Questions

What the Hell is a Monad?

In the programming languages literature, the concept of the monad is widely known and almost as widely misunderstood. Some authors have gone so far as to call monads “the essence of functional programming”, while others seem to think that monads are little more than an especially elaborate kind of syntactic sugar. 5,495 more words

Conceptual Explanations

Four Qualities of a Good Theory

Generally speaking, there are two steps to using any model:

  • Determine whether conditions validate the assumptions of the model. (“Is the model applicable here?”)
  • If conditions do validate the model, determine what predictions can be made. 1,170 more words
  • Interesting Questions

    Security Practice is Not Applied Security Theory, Part 2

    Suppose, for the sake of argument, that security is a system property that can always be specified and implemented. Any model of security entails some notion of misuse of the system, and the very possibility of such misuse implies that the system’s basic structure, as specified and implemented, admits some kinds of use that are simply undesired. 1,742 more words

    Interesting Questions

    Do Abstract Machines Make Abstract Heat?

    It’s fairly well known that the theories of information and of thermodynamics share the concept of entropy in a meaningful way. It is also known, although less well, that the theories of information and of computation also share this concept. 1,829 more words

    Conceptual Explanations