Mike, You have apparently missed the basic idea of "mathematics". The idea is to represent something else in a way that it can be usefully manipulated. OF COURSE there are many ways of representing things, and so long as your mathematics matches your physical reality, they are ALL correct - which was your point. What you missed is that they are all the same in that they are translatable between each other and physical reality. The fact that there is an infinity of them is uninteresting, because all you need do is to simply pick one of them and stick with it.
Continuing... On Mon, Jul 16, 2012 at 4:52 PM, Mike Tintner <[email protected]>wrote: > ** > What, Steve, you're expressing here is the deeply ingrained power of > rational "correct", monistic thinking. That's why I was no doubt > excessively aggressive in tackling it. > > There is no "correct" answer to X+Y=5 - and that's allowing for its use of > variables. > > The reasoning that I applied to 2+2= applies equally here. > No, for any PARTICULAR (valid) mathematical system, there is only one or a small number of (true) solutions. > First, there is no correct way of *numbering* the world - there are > infinite possible numeral systems. > So what?!!! Just pick one - any one. > So in answering your problem, I can switch to alternative numeral systems > if I choose, as I did with 2+2. You can't say I'm "wrong" - "right" and > "wrong" are matters of convention - unless you happen to think you're God > almighty - and it still won't do you any good. > I can sure say you are wrong in whatever system I picked. For example, 2 + 2 =? IV may be correct in Roman numerals, but if I am not using Roman numerals, it is simply WRONG. > And the history of maths is the story of one supposedly "correct" numeral > system and mathematical expression being replaced by another and another. > If it provides an acceptable solution, it is "correct". There are many "correct" systems. At this point, you seem to start jumping to confusions by not seeing the semantic equivalence of seemingly different mathematical systems. Steve =============== > The fundamental metaphysics of this is that we live in a multivious world > - where there are ultimately > > a) a web of infinite causes of any effect > b) a web of infinite consequences for any effect > c) a web of potentially infinite ways to depict any objects (and numbers > are a form of depcition) > d) a web of potentially infinite ways to compare objects > > No one of these is "correct." Any explanation you may offer for a given > effect may be more or less true or false, but it will not be "THE truth." > > In public discourse, rational, monistic thinking still largely reigns - > people are continually saying " this is the right thing to do" - a budget > of 1.2% growth in expenditure is the "right" thing to do - the right way to > promote growth. It's baloney. There are potentially infinite ways to > stimulate the economy. > > "Right-thinking", "rationality" is an extremely limited form of > intelligence. Someone who can only come up with one answer to a problem, > when there are potentially infinite answers is v. limited. > > As soon as you move outside of the artificial systems of logic, maths and > computation, into the realms of real world reasoning, the notion of > "correct" thinking becomes absurd. > > The idea that there is one correct story - one correct version of Romeo & > Juliet, or history of the causes of the last econ. crisis, or one correct > explanation of the birth of computers, or life story of Steve Richfield - > is just a joke. One correct portrait of Obama? > > In all forms of real world reasoning and activity, there are always > multiple conflicting approaches to every problem. > > There is no such thing as a "right" essay - on science, history, > geography, art, philosophy, politics - or any subject in the curriculum. > > To be a real world reasoner, you have to be able to come up with multiple > approaches to any problem, not just one. > > > > > > *From:* Steve Richfield <[email protected]> > *Sent:* Tuesday, July 17, 2012 12:18 AM > *To:* AGI <[email protected]> > *Subject:* Re: [agi] Real World/ Creative Reasoning - what no one gets > about AGI > > Mike, > > On Sun, Jul 15, 2012 at 9:09 AM, Mike Tintner <[email protected]>wrote: > >> ** >> Steve, >> >> There are infinite solutions to 2+2 = >> > > Actually, the "correct" answer is a request for clarification. By the time > my kids were ~6 they learned to, when asked questions like "what is 2 + 2" > to respond with "2 what?, plus two what?". > > Most common questions that people ask are incredibly vague and > presumptive, which leaves the problem you indicated. No, there are NOT an > infinite number of "solutions" to well-understood problems, when a > "solution" is a statement of all possible conditions that satisfy the > constraints. For example, what is the solution to: > > X + Y = 5 > > Obviously, X = 5 - Y > > Depending on Y, X could be almost anything. The solution is like this - > what is needed to satisfy the conditions - which may be VARIABLE. > > Steve > =============== > >> >> 4, FOUR, QUATRE, 1111, 6-2, 7-1, .... , llll [lines], 4.2345 real >> apples .. IV, (and so on in other numeral systems), and so on ad infinitum. >> >> (And the above is not playing around or superficial - there are plenty of >> existing real problems where it is necessary to find an alternative to 4) >> >> There are infinite solutions to every problem. >> >> If you care to take **any real world problem,** in any field, I am quite >> happy to examine it and show you that there are infinite solutions. What is >> the right temperature for the body? There is no right temperature. There >> are self-evidently many temperatures which have pros and cons - and since >> the reality is that there is no such thing as a constant temperature, but >> only a series of fluctuating temperatures, (wh. will presumably also vary >> for different parts of the body) - there are infinite temperatures. >> >> All this is not a matter of opinion - if you care to persist with >> psychological monism, you are saying something that is demonstrably and >> endlessly falsifiable. >> >> And you truly do not get it - >> >> we do not want a robot that can pick up an object in an entirely >> fictional "right" way - that's the kind of industrial narrow AI robot we >> already have - we want an AGI robot that can pick up objects in an endless >> variety of ways - like you, only better, ideally. >> >> Not a robot that can make one right journey to a given goal, but an >> endless variety of journeys, including ever new and better ways. (What's >> the "right" way to tour the US or downtown Las Vegas? If you think there's >> one you are not living in the real world). >> >> Not a machine that can write one description of a scene, but an endless >> range of descriptions - as human writers do.. >> >> Not a machine that can write one program for an activity, but an endless >> range of programs - because that's what is possible and happens in the real >> world of real programs. >> >> You are living mentally in the equivalent of a Flat world in relation to >> AGI. So are most AGI-ers. >> >> Self-evidently, if you think about it, an AGI machine is one that can >> produce an endless diversity of solutions to any problem - not one. >> >> (And the irony is that not even in maths or logic is there one right >> solution to problems, there are endless potential numeral systems and >> logics). >> >> *From:* Steve Richfield <[email protected]> >> *Sent:* Sunday, July 15, 2012 4:13 PM >> *To:* AGI <[email protected]> >> *Subject:* Re: [agi] Real World/ Creative Reasoning - what no one gets >> about AGI >> >> Mike, >> >> On Sun, Jul 15, 2012 at 7:30 AM, Mike Tintner >> <[email protected]>wrote: >> >>> **The mathematics here is slightly out. >>> >>> In the real world, there are actually infinite solutions to any given >>> problem, not one. >>> >> >> Not really. Excluding irrelevant variables, arbitrary ordering, etc., and >> utilizing iterative and recursive representation, real-world problems >> usually have a relatively small number of solutions. My point (and I think >> Ben's points) here is that that solutions must be at a high enough level >> for finite-sized machines (like us) to deal with the "details". Ben is >> trying to do this his way (with narrow AGI) and I am trying to do it my way >> (with high-level representation). What do YOU suggest? >> >>> In the rational realm which exists only in artificial mental and >>> physical worlds, people act as if there is one, but this is purely a >>> **convention.** >>> >>> The solution to a mathematical problem like 2 +2 = ? of "4" is only >>> one of an infinity of possible solutions to that problem. To say "4" is >>> "right" is purely a convention, not an absolute truth. >>> >>> Modern maths, not to mention the entire history of maths, agrees with >>> this - we've been through this here quite a lot - you couldn't have paid >>> attention. >>> >>> If you think there is only one solution to anything, >>> >> >> I don't. What is the square root of 4? Of course, it is +/- 2. Is that >> one solution or two? It all depends on your REPRESENTATION. I suspect that >> the representations in our own heads are quite high level. >> >>> you are, philosophically speaking, extremely narrow-minded, >>> narrow-AI-minded, and not the kind of creative, resourceful, resilient >>> person who can always come up with new solutions to problems - both at a >>> specific and at a general, metacognitive level. >>> >> >> Now that you have demonstrated your complete lack of social skills, not >> to mention your lack of understanding the distinction between multiple >> solutions and single solutions with high-level representation... >> >>> AGI's are not machines that get the "right" solution. Those are narrow >>> AI's. >>> >>> AGI's are and will be creative machines that can endlessly produce new >>> solutions to any given problem, - endlessly give you new ideas. >>> >> >> A MUCH higher level than your thinking is a machine that produces >> seemingly (to us) many solutions simultaneously through high-level >> representation. >> >>> You are still buried in narrow AI. >>> >> >> No, you are still buried in narrow AGI. >> >>> In the real world, in science, technology, arts, history and the >>> entire economy there are not "right" solutions - the ipad isn't the "right" >>> solution to a tablet. There isn't a "right" AGI project. There are >>> "good-and-bad" solutions with pro's and con's, which are more or less >>> profitable and useful. >>> >>> This is a psychologically pluralist world - but our culture hasn't yet >>> fully made the transition, although it's happening relentlessly. We've >>> become culturally pluralist but not yet psychologically pluralist. You and >>> narrow AI are rigid, psychological monists. >>> >>> Shape up, open your mind, broaden your horizons, become a flexible >>> thinker - and completely rethink your approach to AGI. >>> >> >> You should check out your assumptions before letting loose with the >> flames. >> >> Regardless of how good your thoughts might be, jumping on people simply >> cuts you out of the conversations. >> >> Steve >> >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/6952829-59a2eca5> | >> Modify <https://www.listbox.com/member/?&;> Your Subscription >> <http://www.listbox.com> >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/10443978-6f4c28ac> | >> Modify <https://www.listbox.com/member/?&;> Your Subscription >> <http://www.listbox.com> >> > > > > -- > Full employment can be had with the stoke of a pen. Simply institute a six > hour workday. That will easily create enough new jobs to bring back full > employment. > > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/6952829-59a2eca5> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/10443978-6f4c28ac> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Full employment can be had with the stoke of a pen. Simply institute a six hour workday. 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