Question: I've heard the motto [**interaction is more powerful than algorithms**](http://www.cs.brown.edu/people/pw/papers/ficacm.ps) from [Peter Wegner](http://www.cs.brown.edu/~pw/). The basis of the idea is that a (classical) Turing Machine cannot handle interaction, that is, communication (input/output) with the outside world/environment.

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> How can this be so? How can something be more powerful than a Turing Machine? What is the essence of this story? Why is it not more well known?
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Answer: 
Recently ACM held Ubiquity symposium '[What is Computation?](http://ubiquity.acm.org/article.cfm?id=1883611)' in which Peter Wegner published an article which reflects his views on Interactive computing.

Here are two excerpts from the article by Peter Wegner:

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> One new concept, missing from early Turing machines, is "Interactive Computing," which accommodates interaction with the environment during the computation. 
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> Interaction machines can perform more powerful forms of computing than Turing machines, and can perform the kind of thinking proposed by Turing because interaction improves their performance over that of Turing machines.
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However, Fortnow, who has an article in the same symposium, appears to disagree with the Wegner views and believes that interactive computing does not offer any additional power over Turing Machines. 

To add to the mix, it appears that we are still debating and defining computation. Moshe Vardi has an article, What is an Algorithm?, Communications of the ACM, Vol. 55, No. 3, March 2012.

Vardi reports on two new definitions of algorithms. The first is proposed by Gurevich and the second by Moschovakis.

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> Gurevich argued that every algorithm can be defined in terms of an abstract state machine.
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> Moschovakis, in contrast, argued that an algorithm is defined in terms of a recursor, which is a recursive description built on top of arbitrary operations taken as primitives.
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Check this out :)
"***Turing's Ideas and Models of Computations***"
<https://www.cs.montana.edu/~elser/turing%20papers/Turing%27s%20Ideas%20and%20Models%20of%20Computation.pdf>