On Sun, Aug 25, 2019 at 5:00 PM Jose Mario Quintana <jose.mario.quint...@gmail.com> wrote: > > In other words if we could solve problems whose complexity grows > > exponentially, then EMH would be true. Since we can't, we can at least > > classify EMH as not always being useful in the general case. > > Clarify why "Since we can't," then "we can at least classify EMH as not > always being useful in the general case" and what your statement means, in > particular, "being useful" (if you can).
Technically, the phrase "Since we can't" [solve an infinity of problems whose complexity grows exponentially] should be replaced with "Since we haven't" [solved an infinity of problems whose complexity grows exponentially]. But the english language isn't all that great for expressing fine distinctions of this nature. For example: We can't completely prove that the sun will rise tomorrow. Specifically, we know that at some point the sun will stop "rising" - it'll go nova or something, and also, technically, it does not "rise". But with extremely high probability, we'll all be dead by the time the sun goes nova, or the earth stops existing for some other reason, so those are extra words that don't convey much of importance in most conversations. And, meanwhile, the detail about "rising" is one of perspective. The fact that a perspective exists where the earth rotates doesn't eliminate the experience of 'Dawn", and even though there may be a lack of technical vigor to the phrase, many people still find it convenient to talk of the sun "rising". And, we don't get much use out of ideas related to the sun not rising - yeah, it'll eventually happen but so what? Similarly, talking about P=NP issues - in many cases we can work with constrained cases and ignore the lack of generality. We might talk of "boredom" or perhaps use ridicule to dismiss the general case issues, for example. And that's basically what we do with regulations - we dismiss a variety of general case possibilities which makes the remaining cases easier to reason about. Where it gets out of hand is when we start making decisions based on the assumption that "EMH is valid" and and getting into ridiculous territory based on EMH being mathematically valid, instead of "EMH is a handy shorthand way of dismissing some boring/too big/whatever issues". Anyways, when talking about open ended issues, we are forced to take shortcuts, and -- as a result -- even our best efforts are, all too often, inadequate. Thanks, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
