This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of interactive classical algorithms. The modern notion of algorithm was elucidated in the 1930s-1950s. It was axiomatized a quarter of a century ago as the notion of "sequential algorithm"; we call it "classical algorithm" here. The axiomatization was used to show that for every classical algorithm there is a behaviorally equivalent abstract state machine. It was also used to prove the Church-Turing thesis as it has been understood by the logicians. Starting from the 1960s, the notion of algorithm has expanded - probabilistic algorithms, quantum algorithms, etc. - prompting introduction of a much more ambitious version of the Church-Turing thesis commonly known as the "physical thesis." We emphasize the difference between the two versions of the Church-Turing thesis and illustrate how nondeterministic and probabilistic algorithms can be viewed as classical algorithms with appropriate oracles. The same view applies to quantum circuit algorithms and many other classes of algorithms.
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