Mike, This is my one-and-only posting on your thread, in the hopes that you will similarly restrict your comments on my future threads.
As a former Boeing aircraft designer, with some 737 wing and body supports the result of my efforts, I can definitely say that mathematics CAN describe blobs - like 737s. Further, the field of Game Theory depends on making (pseudo) RANDOM decisions based on computed probabilities. There, the goal is NOT to predict the behavior of an adversary who may intentionally be making random decisions, but rather to engineer your own behavior to do as well as possible DESPITE your adversary's behavior. If the result was deterministic, your adversary could/would simply parallel your computations, determine what you plan to do, and engineer a way to make it turn out badly for you. I believe the main flaw in your thinking is contained in the title for this thread. No mathematician uses mathematics "to describe the world" or pieces thereof, if for no other reasons than such descriptions would be nearly worthless. Instead, people use mathematics to engineer strategies and machines to interact with the world, which mathematics works VERY well for, and we have the cars, planes, submarines, etc. to prove it. If your point is that no one will ever be able "to describe the world" with mathematics, I think nearly everyone here would instantly concede that point, but no one here is seeking to do that. People here are seeking to design and build machines that use mathematical methods to INTERACT EFFECTIVELY with the real world, which is a VERY different goal than describing the real world. Sure, a good mathematical description would aid interaction, but even a poor mathematical description is a LOT better than nothing to work with. Sometimes a poor description, when based on sound principles, beats a good empirically based description. You see this in medicine all the time. For most illnesses there are several competing models. One model may be considerably more detailed and technically accurate, but provide NO guidance regarding how to reverse an illness; while another model may be simplistic, yet suggest effective interventions. My work on central metabolic control systems (CMCS) is a perfect example. The simplistic model says that our CMCS must work about as well as theoretically possible just to keep us alive, so any apparent "malfunctions" simply MUST be shortcomings in our own understanding. The complex model fills volumes and has many holes in it. The simplistic model leads us to better understand the "problem" that has apparently "stumped" it, which then leads to twisting the environment in strange ways so that the CMCS gets itself out of its functional hole, while the complex model goes nowhere. Map navigation programs use mathematical methods to compute optimum travel strategies through a heterogeneous world. The people here suspect that extended methods will be able to compute good strategies for far more than travel in the same heterogeneous world. We both think they will fail, especially in the near future, but for differing reasons. However, any claim that no mathematics can be effectively applied to INTERACTING with the real world seems ludicrous, especially in light of all of the OTHER ways that mathematics already interacts so well for. It is really hard to argue with existence proofs - so I suggest that you stop trying. So, this entire discussion is apparently based on the misdirection, from * interacting* to *describing*. I recognize this misdirection and choose to ignore it. What disturbs me the most is that others here apparently do NOT recognize this misdirection, and as a result were drawn into the illogical morass to which it leads. I view this as a sort of IQ test, where people have in effect posted their failures here. Steve ====================== On Wed, Sep 4, 2013 at 6:24 PM, Kyle Kidd <[email protected]> wrote: > """Most mathematicos are bent on insisting that the natural world IS > perfect forms (see Kyle) - that these are eternal and have existed since > the beginning of the universe - when actually they were created a few > thousand years ago at most. Like the kid in the scientific/autistic > experiment, mathematicos/AGI-ers insist on "natural perfection" in a > totally blinkered way while refusing to look at the real world or art, and > looking > only at artificial patterns and maths.""" > > Can you elaborate on what you mean by "natural perfection" and what does > art have to do with engineering machines to do useful tasks? Oscar Wilde > said that "All art is quite useless." While you probably don't agree with > that, it seems to me one of the fundamental reasons art has any value is > that it was created by human hands and conveys something fundamental about > human experience. I don't think art is something that machines must > understand beyond the fact that irrational humans place a very high value > on some useless artifacts. > > > On Wed, Sep 4, 2013 at 7:49 AM, tintner michael > <[email protected]>wrote: > >> The guy says it: >> >> " perfect mathematical forms do not exist in the physical universe" >> >> You guys seem to have a virtual cognitive deficit here. The central point >> of maths was to create perfect forms for the first time which could a) >> serve as standards for measurement and analysis of the world and b) form >> the basis of artificial perfect technological machines,tools and structures >> (like architecture). >> >> Most mathematicos are bent on insisting that the natural world IS perfect >> forms (see Kyle) - that these are eternal and have existed since the >> beginning of the universe - when actually they were created a few thousand >> years ago at most. Like the kid in the scientific/autistic experiment, >> mathematicos/AGI-ers insist on "natural perfection" in a totally blinkered >> way while refusing to look at the real world or art, and looking only >> at artificial patterns and maths. >> >> This is at the centre of AGI - all AGI projects are stuck in part because >> they insist on tackling only "blocks worlds" - artificial, perfect >> mathematically formed worlds. They can't begin to function in - recognize >> or conceptualise - the real, irregular world. Maths doesn't give them the >> tools. So they ignore it. >> >> P.S. The solution to the problem of how to perceive the world in terms >> of fluid schemas and lines (the opposite of maths' rigid patterns and >> lines) lies in *embodied vision/sensory perception.* Or *"bodylines"* and >> "bodyforms". If the lines and forms of the world are perceived as >> guidelines and guideforms for the body, they automatically become fluid >> lines - "loose lines". The reason is that the body - any body - is not >> capable of moving perfectly along perfect lines. So in interpreting any >> line, an embodied viewer has to give "leeway"/"latitude" to the line. An >> embodied viewer/brain knows that when they try to walk along a straight >> line, they are actually going to describe any of a series of more or less >> crazy lines. >> >> You could say that maths was invented to correct this weakness of animal >> and human movement - but this weakness is also a great strength. It's a >> great strength not to have interpret things rigidly, but be able to see >> them loosely fluidly. >> >> This isn't an either/or matter. We need both rigid, math, disembodied >> vision and fluid, artistic, embodied vision - narrow, rigid, AI and >> broad, fluid, AGI. But maths' rigid forms are not AGI - they are the >> opposite. >> >> >> >> >> On 4 September 2013 12:11, Kyle Kidd <[email protected]> wrote: >> >>> Mathematics is a human created tool used to create abstract models that >>> act like some of the complex systems found in nature. The shortfall of >>> mathematics isn't the art itself, but the inability of the human >>> practitioner to account for every variable in every unique instance that >>> might occur, and to identify which model corresponds to the starting point >>> being studied. Models can be generalized to predict what is most likely to >>> occur in a given scenario but this doesn't imply any absolute understanding >>> of reality, only an understanding of how a few isolated variables affect >>> each other with many constraints built into the solution. >>> >>> Only an omnipotent being/machine could have all this information along >>> with a perfect understanding of the effects of all discrete entities in the >>> system itself to come up with a perfect solution for every possible >>> starting point. >>> >>> >>> >>> >>> On Wed, Sep 4, 2013 at 6:07 AM, tintner michael < >>> [email protected]> wrote: >>> >>>> [The main point is missed: maths cannot find the "formula"/"prototype" >>>> for irregular (and by extension) creative forms [like rocks and blobs] or >>>> irregular groups of forms - patchworks. The natural world consists of >>>> irregular forms and irregular patchworks. There is no formula for them - >>>> only fluid schemas. The human/AGI mind is adapted to and designed for an >>>> irregular, patchwork world not the regular, patterned, "blocks" world of >>>> AGI-ers' blind fantasies]. >>>> >>>> >>>> Is mathematics an effective way to describe the world? >>>> September 3rd, 2013 in Other Sciences / Mathematics >>>> >>>> Math has the illusion of being effective when we focus on the >>>> successful examples, Abbott argues. But there are many more cases where >>>> math is ineffective than where it is effective. Credit: Derek Abbott. ©2013 >>>> IEEE >>>> >>>> Mathematics has been called the language of the universe. Scientists >>>> and engineers often speak of the elegance of mathematics when describing >>>> physical reality, citing examples such as ?, E=mc2, and even something as >>>> simple as using abstract integers to count real-world objects. Yet while >>>> these examples demonstrate how useful math can be for us, does it mean that >>>> the physical world naturally follows the rules of mathematics as its >>>> "mother tongue," and that this mathematics has its own existence that is >>>> out there waiting to be discovered? This point of view on the nature of the >>>> relationship between mathematics and the physical world is called >>>> Platonism, but not everyone agrees with it. >>>> >>>> Derek Abbott, Professor of Electrical and Electronics Engineering at >>>> The University of Adelaide in Australia, has written a perspective piece to >>>> be published in the Proceedings of the IEEE in which he argues that >>>> mathematical Platonism is an inaccurate view of reality. Instead, he argues >>>> for the opposing viewpoint, the non-Platonist notion that mathematics is a >>>> product of the human imagination that we tailor to describe reality. >>>> >>>> This argument is not new. In fact, Abbott estimates (through his own >>>> experiences, in an admittedly non-scientific survey) that while 80% of >>>> mathematicians lean toward a Platonist view, engineers by and large are >>>> non-Platonist. Physicists tend to be "closeted non-Platonists,**" he >>>> says, meaning they often appear Platonist in public. But when pressed in >>>> private, he says he can "often extract a non-Platonist confession." >>>> >>>> So if mathematicians, engineers, and physicists can all manage to >>>> perform their work despite differences in opinion on this philosophical >>>> subject, why does the true nature of mathematics in its relation to the >>>> physical world really matter? >>>> >>>> The reason, Abbott says, is that because when you recognize that math >>>> is just a mental construct-just an approximation of reality that has its >>>> frailties and limitations and that will break down at some point because >>>> perfect mathematical forms do not exist in the physical universe-then you >>>> can see how ineffective math is. >>>> >>>> And that is Abbott's main point (and most controversial one): that >>>> mathematics is not exceptionally good at describing reality, and definitely >>>> not the "miracle" that some scientists have marveled at. Einstein, a >>>> mathematical non-Platonist, was one scientist who marveled at the power of >>>> mathematics. He asked, "How can it be that mathematics, being after all a >>>> product of human thought which is independent of experience, is so >>>> admirably appropriate to the objects of reality?" >>>> >>>> In 1959, the physicist and mathematician Eugene Wigner described this >>>> problem as "the unreasonable effectiveness of mathematics.**" In >>>> response, Abbott's paper is called "The Reasonable Ineffectiveness of >>>> Mathematics.**" Both viewpoints are based on the non-Platonist idea >>>> that math is a human invention. But whereas Wigner and Einstein might be >>>> considered mathematical optimists who noticed all the ways that mathematics >>>> closely describes reality, Abbott pessimistically points out that these >>>> mathematical models almost always fall short. >>>> >>>> What exactly does "effective mathematics" look like? Abbott explains >>>> that effective mathematics provides compact, idealized representations of >>>> the inherently noisy physical world. >>>> >>>> "Analytical mathematical expressions are a way making compact >>>> descriptions of our observations,**" he told Phys.org. "As humans, we >>>> search for this 'compression&#**39; that math gives us because we have >>>> limited brain power. Maths is effective when it delivers simple, compact >>>> expressions that we can apply with regularity to many situations. It is >>>> ineffective when it fails to deliver that elegant compactness. It is that >>>> compactness that makes it useful/practical ... if we can get that >>>> compression without sacrificing too much precision. >>>> >>>> "I argue that there are many more cases where math is ineffective >>>> (non-compact) than when it is effective (compact). Math only has the >>>> illusion of being effective when we focus on the successful examples. But >>>> our successful examples perhaps only apply to a tiny portion of all the >>>> possible questions we could ask about the universe." >>>> >>>> Some of the arguments in Abbott's paper are based on the ideas of the >>>> mathematician Richard W. Hamming, who in 1980 identified four reasons why >>>> mathematics should not be as effective as it seems. Although Hamming >>>> resigned himself to the idea that mathematics is unreasonably effective, >>>> Abbott shows that Hamming'**s reasons actually support non-Platonism >>>> given a reduced level of mathematical effectiveness. >>>> >>>> Here are a few of Abbott's reasons for why mathematics is reasonably >>>> ineffective, which are largely based on the non-Platonist viewpoint that >>>> math is a human invention: >>>> >>>> . Mathematics appears to be successful because we cherry-pick the >>>> problems for which we have found a way to apply mathematics. There have >>>> likely been millions of failed mathematical models, but nobody pays >>>> attention to them. ("A genius," Abbott writes, "is merely one who has a >>>> great idea, but has the common sense to keep quiet about his other thousand >>>> insane thoughts."**) >>>> >>>> . Our application of mathematics changes at different scales. For >>>> example, in the 1970s when transistor lengths were on the order of >>>> micrometers, engineers could describe transistor behavior using elegant >>>> equations. Today's submicrometer transistors involve complicated effects >>>> that the earlier models neglected, so engineers have turned to computer >>>> simulation software to model smaller transistors. A more effective formula >>>> would describe transistors at all scales, but such a compact formula does >>>> not exist. >>>> >>>> . Although our models appear to apply to all timescales, we perhaps >>>> create descriptions biased by the length of our human lifespans. For >>>> example, we see the Sun as an energy source for our planet, but if the >>>> human lifespan were as long as the universe, perhaps the Sun would appear >>>> to be a short-lived fluctuation that rapidly brings our planet into thermal >>>> equilibrium with itself as it "blasts" into a red giant. From this >>>> perspective, the Earth is not extracting useful net energy from the Sun. >>>> >>>> . Even counting has its limits. When counting bananas, for example, at >>>> some point the number of bananas will be so large that the gravitational >>>> pull of all the bananas draws them into a black hole. At some point, we can >>>> no longer rely on numbers to count. >>>> >>>> . And what about the concept of integers in the first place? That is, >>>> where does one banana end and the next begin? While we think we know >>>> visually, we do not have a formal mathematical definition. To take this to >>>> its logical extreme, if humans were not solid but gaseous and lived in the >>>> clouds, counting discrete objects would not be so obvious. Thus axioms >>>> based on the notion of simple counting are not innate to our universe, but >>>> are a human construct. There is then no guarantee that the mathematical >>>> descriptions we create will be universally applicable. >>>> >>>> For Abbott, these points and many others that he makes in his paper >>>> show that mathematics is not a miraculous discovery that fits reality with >>>> incomprehensible regularity. In the end, mathematics is a human invention >>>> that is useful, limited, and works about as well as expected. >>>> >>>> For those who seek something more practical out of such a discussion, >>>> Abbott explains that this understanding can allow for greater freedom of >>>> thought. One example is an improvement of vector operations. The current >>>> method involves dot and cross products, "a rather clunky" tool that does >>>> not generalize to higher dimensions. Lately there has been a renewed >>>> interest in an alternative approach called geometric algebra, which >>>> overcomes many of the limitations of dot and cross products and can be >>>> extended to higher dimensions. Abbott is currently working on a tutorial >>>> paper on geometric algebra for electrical engineers to be published in the >>>> near future. >>>> >>>> More information: More information: Derek Abbott. "The Reasonable >>>> Ineffectiveness of Mathematics.**" Proceedings of the IEEE. To be >>>> published. DOI: 10.1109/JPROC.**2013.2274907 >>>> >>>> © 2013 Phys.org >>>> >>>> "Is mathematics an effective way to describe the world?." September >>>> 3rd, 2013. http://phys.**org/news/**2013-09-mathemat**ics-effective-** >>>> world.html<http://phys.org/news/2013-09-mathematics-effective-world.html> >>>> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >>>> <https://www.listbox.com/member/archive/rss/303/12578217-f409cecc> | >>>> 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/303/6952829-59a2eca5> | >>> 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/303/12578217-f409cecc> | >> 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. 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