> Unless you really do want a way to talk about inconsistencies—then you might try Paraconsistent Logic. The idea of paraconsistency is that coherence is possible even without consistency. Put another way, a paraconsistent logician can say that a theory is inconsistent without meaning that the theory is incoherent, or absurd. (perhaps expressly designed for those that are pro-life and pro capital punishment)
( Or for those that are contra-life and contra capital punishment? Or for attendees arriving in private jets and yachts to the "super-secret" Google Camp conference on climate (do not google Google Camp)? ;) On Fri, Sep 6, 2019 at 9:54 AM Donna Y <[email protected]> wrote: > > The obscure and tedious way of mathematical language was designed to be unambiguous. > > > It's difficult to talk about mathematical statements which are inconsistent, in a consistent fashion. > > > That’s because whenever a statement is inconsistent in mathematics, it gets tossed. A contradiction is a sentence together with its negation, and a theory is inconsistent if it includes a contradiction. Consider also the logical principle ex contradictione quodlibet (ECQ) (from a contradiction every proposition may be deduced--also recently called explosion). > > Unless you really do want a way to talk about inconsistencies—then you might try Paraconsistent Logic. The idea of paraconsistency is that coherence is possible even without consistency. Put another way, a paraconsistent logician can say that a theory is inconsistent without meaning that the theory is incoherent, or absurd. (perhaps expressly designed for those that are pro-life and pro capital punishment) > > Lets break down the statement “if we could solve problems whose complexity grows exponentially, then EMH would be true.” > > If P then Q > > P: > > > In 1965, Jack Edmonds [13] gave an efficient algorithm to solve this matching problem and suggested a formal definition of “efficient computation” (runs in time a fixed poly- nomial of the input size). The class of problems with efficient solutions would later become known as P for “Polynomial Time”. > > > > Computational complexity describes the time or space it takes to run an algorithm. > > > ...the known algorithms for many basic problems within P, including Frechet distance, edit distance, string matching, k-dominating set, orthogonal vectors, stable marriage for low dimensional ordering functions, and many others, are essentially optimal. > > > > > We were thinking about distinguishing very hard problems, such as NP-complete problems, from relatively easy problems, such as those in P. > Anyway the equalities of complexity classes translate upwards. For example, if P=NP, then EXP=NEXP. > > >>>>>> Since we can't > > > 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. > > Several NP-complete problems have exponential algorithms. > > Peter Shor’s algorithm finds the prime factors of an integer P. (effectively breaking RSA.) Previously the runtime was exponential—given call to Quantum computer—it would be polynomial. > > Shor's Algorithm in Quantum Computing - Topcoder > > https://www.topcoder.com/blog/shors-algorithm-in-quantum-computing/ < https://www.topcoder.com/blog/shors-algorithm-in-quantum-computing/> > > But what we need is an algorithm for an NP-complete problem that runs in polynomial time. > > We do not have that yet and it appears beyond the currently known techniques. > > Current approaches to the P vs NP problem are disguised forms of problems in cryptanalysis. In order to prove a function f is not in a complexity class C, exhibit some combinatorial property of f that provably prevents it from being in the class C. > > > So let’s say in future we did have a solution. > > If P then Q > > P > then Q > > Except on what basis did we establish P then Q ? > > Nowhere. > > P is independent of Q. > > P(A|B)=P(A)--the occurrence of B has no effect on the likelihood of A. Whether or not the event A has occurred is independent of the event B. > > So evaluate EMH as independent. > > The newer definition of efficient financial markets is that such markets do not allow investors to earn above-average returns without accepting above-average risks. > > Whatever patterns or irrationalities in the pricing of individual stocks that have been discovered in a search of historical experience are unlikely to persist and will not provide investors with a method to obtain extraordinary returns. > > Ah—risk adjusted. > Ah—all patterns disappear and can’t be exploited. > > If that is the case—EMH is true because it is a tautology. > > > tautology | tɔːˈtɒlədʒi | > > noun (plural tautologies) [mass noun] > > the saying of the same thing twice over in different words, generally considered to be a fault of style (e.g. they arrived one after the other in succession). > > • [count noun] a phrase or expression in which the same thing is said twice in different words. > > • Logic a statement that is true by necessity or by virtue of its logical form. > > Donna Y > [email protected] > > > > On Sep 5, 2019, at 6:06 PM, Raul Miller <[email protected]> wrote: > > > > On Thu, Sep 5, 2019 at 6:03 PM Jose Mario Quintana > > <[email protected]> wrote: > >> 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), > > > > Yeah, that carries a lot of assumptions with it. > > > > It's difficult to talk about mathematical statements which are > > inconsistent, in a consistent fashion. > > > > Thanks, > > > > -- > > Raul > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
