In the fictional dialogue, Claude Shannon’s first answer is more correct—info theory is useful far outside the original domain of application, and its elegance is the best way to predict that.
I disagree. Consider the following two sources of evidence that information theory will be broadly useful:
Information theory is elegant.
There is some domain of application in which information theory is useful.
I think that (2) is stronger evidence than (1). If some framework is elegant but has not been applied downstream in any domain after a reasonable amount of time, then I don’t think its elegance is strong reason to nevertheless believe that the framework will later find a domain of application.
I think there’s some threshold number of downstream applications X such that once a framework has Xdownstream applications, discovering the (X+1)st application is weaker evidence of broad usefulness than elegance. But very likely, X≥1. Consider e.g. that there are many very elegant mathematical structures that aren’t useful for anything.
In the fictional dialogue, Claude Shannon’s first answer is more correct—info theory is useful far outside the original domain of application, and its elegance is the best way to predict that.
I disagree. Consider the following two sources of evidence that information theory will be broadly useful:
Information theory is elegant.
There is some domain of application in which information theory is useful.
I think that (2) is stronger evidence than (1). If some framework is elegant but has not been applied downstream in any domain after a reasonable amount of time, then I don’t think its elegance is strong reason to nevertheless believe that the framework will later find a domain of application.
I think there’s some threshold number of downstream applications X such that once a framework has Xdownstream applications, discovering the (X+1)st application is weaker evidence of broad usefulness than elegance. But very likely, X≥1. Consider e.g. that there are many very elegant mathematical structures that aren’t useful for anything.