On Fri, Sep 6, 2019 at 9:54 AM Donna Y <[email protected]> wrote: > Lets break down the statement “if we could solve problems whose complexity > grows exponentially, then EMH would be true.”
That was a colloquial english statement. If you want to treat it as a mathematical statement you must first gather the axioms which it was reflecting. > Computational complexity describes the time or space it takes to run an > algorithm. Yes. And with simplifying assumptions which only approximate the real world conditions it's expected to be describing. For example, when we use O(n) to describe a calculation, we have usually assumed fixed width arithmetic which usually implies a fixed ceiling, which would imply O(1) if we wanted to describe that ceiling, or something like O(n*ln n) if we wanted to allow arbitrary precision arithmetic (though memory bounds would get us back to O(1), if we cared about them). I bring this up to point out that mathematical relevance is tied to focus of attention. Skipping back to EMH -- it can be a fancy way of saying "most ideas are crud". And, when you start bringing in historical examples, focusing on practical issues, we can often see this playing out. Most people don't need what we're selling but with sufficient salesmanship a number of them can be convinced to buy. But, do that enough, and you start getting backlash from people who realized that what they thought they were getting was not what they got. This can give us the s-curve that most people learn about in business school. But focusing on EMH as the reason for purchase decisions would tend to miss out on this view of things. > But maybe we can. A computer algorithm might use brute force to go through > all available options. Humans automatically search for a solution that > intuitively feels right. Brute force works within limits. Approximated brute force extends those limits but starts to carry risks of going wrong. Depending on how far you push it that risk can become significant. Sometimes though you don't have any better options. > If that is the case—EMH is true because it is a tautology. If it's a tautology, we can ignore it and focus instead on the underlying axioms (or on whatever else we deem important). Thanks, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
