But when we talk about ways that an AGI program might learn to recognize different KINDS of patterns we aren't usually referring to the concept of a pattern that is an image which is repeated over and over again and don't usually mean that we would use a mathematical formula per se or a pure mathematical formula, or to a method that could create every kind of pattern (or patchwork) possible, we are usually referring to a simple method that would approximate a pattern that the program had seen. - Jim Bromer
On Wed, Sep 4, 2013 at 12:16 PM, Mike Archbold <[email protected]> wrote: > A lot of the posts on strong AI are geared to argue that such-and-such > approach is inadequate, but such-and-such approach will work. But you > don't see as many posts that say such-and-such approach may be > partially adequate. I view mathematics that way -- it does a lot but > it doesn't do everything. > > It seemed like for a while narrow AI became more and more > mathematical, with authors first saying "given some problem with this > contraint under these conditions" they then flash their formula, > seemingly to show their in-group membership, guaranteeing that > somebody that didn't know differential calculus would get lost. The > tacit assumption being that math-first is the way to go and it does > everything. > > Mike A > > On 9/4/13, 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 >> RSS Feed: https://www.listbox.com/member/archive/rss/303/11943661-d9279dae >> Modify Your Subscription: >> https://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com >> > > > ------------------------------------------- > AGI > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/24379807-f5817f28 > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
