Donna wrote: > The converse of "If it rains, then they close the windows" is "If they close the windows, then it rains.” > > Raining induces people to close windows but closing windows doesn’t induce it to rain. > > You need to prove both P and Q directly because the converse of P then Q is not always true.
I, of course, agree. One of my favorite examples is: If it is snowing, then it is cold. However, if it is cold, then it is not necessarily snowing (particularly in the middle of Antartica!). That is why the claim, > > > 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. Does not make any sense to me despite the expounding below (even assuming that the claim "if we could solve problems whose complexity grows exponentially, then EMH would be true" holds, which I regard as very misleading), > > 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 On Wed, Sep 4, 2019 at 2:19 PM Donna Y <[email protected]> wrote: > > Maymin says: > > The strategy we will follow for a given input is to merely place the encoding orders in the market, wait some constant amount of time, and then cancel all outstanding orders and liquidate any positions we have. Because we are trading minimum lot sizes, the liquidation cost is minimal. > > > > So what should the market do? If it is truly efficient, and there exists some way to execute all of those separate OCO orders in such a way that an overall profit is guaranteed, including taking into account the larger transactions costs from executing more orders, then the market, by its assumed efficiency, ought to be able to find a way to do so. > > > > In other words, the market allows us to compute in polynomial time the solution to an arbitrary 3-SAT problem. > > > Quick order matching would demonstrate transactional market efficiency but EMF is concerned with information efficiency. Evaluating profit does make it necessary to evaluate if there’re profits or losses due to the spread and weather they could be exploited if that is part of the way information efficiency is evaluated. > > Evaluated weak-form EMF entails the effect of historic data—something not available for a transaction that might be available in the future. > > > > > And this seems like an at least somewhat sensible position, since > > regulations limit or eliminate possibilities, and thus can eliminate > > or reduce the sort of exponential growth in possibilities that he was > > describing. > > > > In other words, market regulations eliminate NP-Completeness (among > > other things). > > Market regulation aim to make the market competitive and fair as well as efficient. What they may want to eliminate if a loophole that would allow one or more participants to drain money from other participants unfairly and also undermine the primary purpose of the market which is to raise capital for firms. > > > The primary role of the capital market is allocation of ownership of the economy's capital stock. (Fama 1970) > > The converse of "If it rains, then they close the windows" is "If they close the windows, then it rains.” > > Raining induces people to close windows but closing windows doesn’t induce it to rain. > > You need to prove both P and Q directly because the converse of P then Q is not always true. > > Even if market regulations eliminate market efficiency it is definitely false that > market regulations eliminate NP-Completeness > > > > That said, it's also worth noting that mathematics is not science. And > > > it's science which concerns itself with testability, not math (outside > > > of specific specializations, such as probability and statistics, which > > > attempt to model tests, with varying degrees of success). > > > > Economics is not mathematics—it is a social science attempting to explain social phenomena and distribution of resources among people. > > Computational complexity theory is a subfield of theoretical computer science > > Both Economics and Computer Science use Mathematics. > > Testing a hypothesis in science is a decision problem in mathematics. > > Donna Y > [email protected] > > > > On Sep 4, 2019, at 12:09 PM, Raul Miller <[email protected]> wrote: > > > > The reason you won't see orders like that in the historic record is > > that regulations on the market have not allowed orders of that sort. > > > > So if that is the nature of the flaw we find in his reasoning, what we > > would essentially be saying is that if EMH is valid, EMH depends on > > market regulations to remain valid. > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
