EFTA02607711

From: Joscha Bach Sent: Monday, December 31, 2018 4:54 PM To: Jeffrey Epstein Subject: Re: This is the solution of =he TSP for all towns of the US that have more than 500 =esidents: The fact that TSP is NP =ard does not mean that it cannot be approximated efficiently, and even =olved for most practical cases. Amoebas and many other biological =ystems can often implement a parallel graph traversal that gives a good =nough solution for a TSP like problem. However, approximate solutions =o TSP cannot usually mapped to solutions to other NP hard problems =i.e. crypto). l=suspect that we are not on the same page wrt the nature and scope of =omputation. The way I see it, mathematics is the domain of all languages. =11 modeling takes place in a language, so modeling (including thinking, =hich is a kind of modeling) is a subset of mathematics. "Classical =athematics" is a branch of math that has "time-less" semantics, i.e. =he mapping between the a statements and its semantics (for instance, =he axioms that a statement can be reduced to in a proof) can take an =rbitrary number of steps, including infinitely many. Godel could =how that if we allow self referential statements, we cannot always =uarantee that the proof does not lead to contradictions and the =emantics of the statement become undecidable. Turing generalized =0del's idea and demonstrated that the problem crops up once the =roof can have infinitely many steps, i.e. a machine that performs the =roof is not guaranteed to terminate its execution. These problems at the =oundations of classical mathematics disappear once we switch to =onstructive mathematics. We can recover the functionality of classical =athematics (like geometry, real numbers and continuous transitions) by =eplacing all entities that require infinite numbers of steps to =enerate by generator functions, and distinguish between values and =unctions. Evaluating a function comes at a cost that is being left to =he one that wants to determine an approximate value. Constructive mathematics =nd computation are the same thing. In computation, performing a =ransformation in a language comes at a non-zero cost, and infinite-cost =ransitions cannot be made. My proposal is simply that the languages in which we =escribe our observations at the foundational level should be =omputational. (Constructive math is the subset of math that works, and =odeling and thinking are subsets of constructive math.) I found that many =athematicians (including Hilbert) have been constructivists for a long =ime, because they were aware of the implications of Godel's proof =nd how to deal with it. Chaitin and others have since done a lot of =ork in exploring the equivalence of computation and "math that works". =n my view, mathematics is a code library for thinking, with a bug that =as discovered and resolved in the first half of the last century. =owever, most physicists are using that code library without being aware =f that bug and its resolution, which may have contributed to the issues =n foundational physics that prevent physicists from solving the =uzzle. Our =uman minds seem to have two separate modeling systems: one is =erceptual, and it optimizes for coherence, i.e. consistency with the =ensory input and within the model that predicts the sensory input. We =re always in a possible universe, where possible refers to a state in =hich all the present perceptual elements are compatible with each =ther. EFTA_R1_01799696 EFTA02607711 Reasoning is a separate system that repairs =erception, whenever the perception is inconsistent. Reasoning optimizes =or truth, i.e. some kind of proof, which is more narrow than coherence. =The perceptual system does not spell out its axioms.) Mathematics =ormalizes subsets or reasoning and perception in ways that always =flows proofs, usually at the cost of using a discrete low dimensional =odeling language. When we talk about things like "culture", we tend to =se language where the symbols are less narrowly defined. Wittgenstein's =roject was to fix that by recovering a semantics of natural language =hat is amenable to proof. By his own estimate, he did not succeed. =arvin had the same goal, and I think he did try until the end. The =olution might be to give up on natural language as the primary carrier =f thought, and use a perceptual language instead, upon which we anchor =he natural language as a tool for disambiguation. Let me know when there =s a good time for skype. J On Dec 30, 2018, at 07:40,1 <[email protected]> wrote: as the traveling salesman is np =oes the ameoba still compute???? or do you assume =olving a problem , is always a computation. ? is kissing =omeone a computation? does computation always involve =easurement? . is perception a computation , or is =hougt a computation.? is culture a computation. ? Im =egining to think that the things that we cant measure are =ubject to different rules On Sun, =ec 30, 2018 at 7:29 AM Joscha Bach wrote: Sure! Will =e back late tonight. Tomorrow? Am =0.12.2018 um 13:22 schrieb J <[email protected]>: ok =nbsp;skype me when you have time. On Sun, Dec 30, 2018 at 7:21 AM Joscha Bach wrote: On the way back from =ermany to Boston (was here for three days to give an invited talk at =he Chaos Communication Congress). Am =0.12.2018 um 12:18 schrieb 1 <[email protected]>: where are =ou? On Sun, Dec 30, 2018 at =:07 AM Joscha Bach wrote: This year's installment of the Computation to =onsciousness series. Thank you! Joscha 2 EFTA_R1_01799697 EFTA02607712 Am 30.12.2018 urn 00:16 schrieb J [email protected]>: https://www.popularmechanics.com/science/math/a25686417/amoeba-=ath/ =lease note The information contained in this =ommunication is confidential, may be attorney-client =rivileged, may constitute inside information, and is =ntended only for the use of the addressee. It is the =roperty of JEE Unauthorized use, disclosure =r copying of this communication or any part thereof is =trictly prohibited and may be unlawful. If you have =eceived this communication in error, please notify us =mmediately by return e-mail or by e-mail =o [email protected], and destroy this =ommunication and all copies thereof, including all =ttachments. copyright -all rights reserved =nbsp; please note The information contained in this =ommunication is confidential, may be attorney-client =rivileged, may constitute inside information, and is =ntended only for the use of the addressee. It is the =roperty of JEE Unauthorized use, disclosure =r copying of this communication or any part thereof is =trictly prohibited and may be unlawful. If you have =eceived this communication in error, please notify us =mmediately by return e-mail or by e-mail =o [email protected], and destroy this =ommunication and all copies thereof, including all =ttachments. copyright -all rights reserved =nbsp; please note The information contained in this =ommunication is confidential, may be attorney-client =rivileged, may constitute inside information, and is =ntended only for the use of the addressee. It is the =roperty of JEE Unauthorized use, disclosure =r copying of this communication or any part thereof is =trictly prohibited 3 EFTA_R1_01799698 EFTA02607713 and may be unlawful. If you have =eceived this communication in error, please notify us =mmediately by return e-mail or by e-mail =o [email protected], and destroy this =ommunication and all copies thereof, including all =ttachments. copyright -all rights reserved =nbsp; please note The information contained in this =ommunication is confidential, may be attorney-client =rivileged, may constitute inside information, and is =ntended only for the use of the addressee. It is the =roperty of JEE Unauthorized use, disclosure =r copying of this communication or any part thereof is =trictly prohibited and may be unlawful. If you have =eceived this communication in error, please notify us =mmediately by return e-mail or by e-mail =o [email protected], and destroy this =ommunication and all copies thereof, including all =ttachments. copyright -all rights reserved 4 EFTA_R1_01799699 EFTA02607714