> > Pattern and formula correspond. A pattern can be expressed as a formula.
To describe something in mathematical form, you have both a formula (say, a function that generates the target form from a set of parameters) and a set of parameters passed to the formula. So the description of the form is not just a formula. And you are saying there *are* regularities to a group of irregular forms – > without identifying those regularities. Not so. I just described the regularities in English. Did you actually read what I wrote? Here, let me repeat it for you: I can't see that entire image, since I'm on my phone, but in what I can see of it, you have various closed loops, maybe with other closed loops inside them that don't touch the outer ones. These could be thought of as outlines of shapes. So the common schema, in mathematical terms, is "an enclosed area with countable areas inside it that have been excluded". Thus, we have (1) an outer boundary, which is a loop, a continuous path which can be described to any level of approximation by a sequence of points, as is done by the very image format which allowed you to present these blobs to the group in the first place, and (2) zero or more inner boundaries, also described by loops, with the restriction that they are inside the outer loop, and none of the loops touch each other. (They don't have any points in common.) The definition of "inside" is probably the most difficult to express in mathematics of the concepts required here. I would refer you to any analytic geometry book for a *formal* definition of the various concepts I've used. They have already been defined, and so the shapes you gave are fairly straight forward to handle algorithmically. So in a program, what I would end up with is a set of point vectors, one describing the outer curve and the others describing inner curves, if any. This collection of vectors can then be checked algorithmically using something as simple as the Paint program's color fill function to verify the constraints are met. The regularities are captured in what I've said above. If you can't see that, it's because you're refusing to. The definition you offer for a blob schema doesn’t work - it also > embraces regular geometrical forms *and* simple drawings of faces – it > can’t identify just irregular blobs. Changing the problem to make it more complicated *after* I've already provided the solution doesn't invalidate the fact that I just provided a solution to the original problem. If we go down this path, when I provide a mathematical description of a simple drawing of a face, and modify the recognition algorithm to exclude cases recognized by this secondary pattern, I can trust that you're simply going to declare that the problem is more complicated than originally stated and add something else post hoc. I'm not trying to provide you with a universal classification algorithm for all types of shapes. I'm simply trying to demonstrate to you that math is up to the task of solving a problem you said it couldn't solve: capturing the regularities present in the shapes you provided. It also doesn’t explain something interrelated which I left out – which is > your capacity to recognize INDIVIDUAL blobs. You can retain and recognize, > for example, the individual, somewhat blob-like shape of the U.S. or Italy, > and you could retain any of the shapes I drew if you wished. Changing the problem post hoc again, but this time the method I described is already up to the task without further modification. Above I pointed out that the "blobs" can be represented as point vectors. All we have to do is compare these point vectors against each other to see how similar they are, much as handwriting recognition software and other gesture-based interfaces have been doing for years. (They actually use this sort of point vector.) We can easily store these vectors for future recognition, and set any arbitrary threshold of similarity for recognizing the shapes as being reoccurrences of the original. Fundamental to a real AGI is the capacity to recognize individuals of all > kinds as individuals. – and you do that by retaining the whole irregular > form – as you do with Italy. Irregularities define individuals. Once again, this is handled by decomposing the individual down into *2* pieces, function + parameters, not just 1, the function/formula. The function represents the regularities identified in the shape, and the parameters represent the irregularities. They can easily be put back together to rebuild the original. Nothing is lost. Individuals are fundamental to the movie of consciousness – that’s what > you’re looking at all the time – not just classes, but individuals in > individual scenes this bloke you know, that tree in your backyard, this > lawn of yours, this house of yours and so on. No argument here. Of *course *it's instances, not just classes. Nobody said otherwise. The idea that the human brain does this by reducing each and every form to > a mathematical formula/algo or whatever is frankly absurd – it’s > grotesquely inefficient and complicated, it doesn’t work – because as soon > as you reduce a form to a formula, you lose the form/the whole, and the > relevant maths was only invented at most a few thousand years ago, if not > actually only decades ago. Algorithms widely vary in their efficiency. Some are intractable, and some are fast. There is usually a fast one, and it just takes time to find it. If there isn't, we wait until hardware is faster. Nature faces the same problem in the same way when designing organisms. Formulas, on the other hand, are divorced from efficiency (unless you're looking at description length), because their purpose is expression, not computation. Any representation that is grotesquely inefficient and complicated is a bad choice, and we will choose (or design) one that *simplifies *solving the problem, rather than complicating it based specifically on that criterion. Reducing to a formula does indeed lose the form/the whole. This is because you've forgotten the other half of the decomposition: the parameters. With that omission, it's no wonder you can't see how mathematics could be used to describe arbitrary forms. You think if we use math we're helplessly forced to throw away all that information even if it's useful. This is not the case. Pointing out the recency of the mathematical techniques is hardly an argument against them. Invention takes time, and usually the better ones come later, not earlier. So really you are indeed in the end just saying “maths will work.;.” and > in no way getting to grips with why we/AGI are so horribly stuck.. No, that's just all you're hearing because your mind is closed. I provided justifications to back up the claim. You dismissed them without really thinking about what I was saying, something you are fond of accusing everyone else of doing. On Tue, Nov 6, 2012 at 2:52 PM, Mike Tintner <[email protected]>wrote: > Well, your position is really no different from what I am arguing > against. > > Pattern and formula correspond. A pattern can be expressed as a formula. > > And you are saying there *are* regularities to a group of irregular forms > – without identifying those regularities. > > The definition you offer for a blob schema doesn’t work - it also > embraces regular geometrical forms *and* simple drawings of faces – it > can’t identify just irregular blobs. > > It also doesn’t explain something interrelated which I left out – which is > your capacity to recognize INDIVIDUAL blobs. You can retain and recognize, > for example, the individual, somewhat blob-like shape of the U.S. or Italy, > and you could retain any of the shapes I drew if you wished. > > Fundamental to a real AGI is the capacity to recognize individuals of all > kinds as individuals. – and you do that by retaining the whole irregular > form – as you do with Italy. Irregularities define individuals. > > Individuals are fundamental to the movie of consciousness – that’s what > you’re looking at all the time – not just classes, but individuals in > individual scenes this bloke you know, that tree in your backyard, this > lawn of yours, this house of yours and so on. > > The idea that the human brain does this by reducing each and every form to > a mathematical formula/algo or whatever is frankly absurd – it’s > grotesquely inefficient and complicated, it doesn’t work – because as soon > as you reduce a form to a formula, you lose the form/the whole, and the > relevant maths was only invented at most a few thousand years ago, if not > actually only decades ago. > > So really you are indeed in the end just saying “maths will work.;.” and > in no way getting to grips with why we/AGI are so horribly stuck.. > > *From:* [email protected] > *Sent:* Tuesday, November 06, 2012 2:18 PM > *To:* AGI <[email protected]> > *Subject:* Re: [agi] Randomness: Mathematics as Perceptual Bias > > Must you revert to insults and YELLING again? I thought we had that out > already. However much you can't stand it that we don't agree with you, that > doesn't mean a single one of us has a cognitive deficit. > > It is quite easy to see that irregularity is different from regularity. > The previous message I wrote was designed to point out to you that > irregularities are decorations to regularities, and it is the regularities > which determine the COMMON SCHEMA. But instead you missed it & essentially > calle me & everyone else on this list idiots. > > You are utterly and completely correct that there is no formula which > describes those shapes. While technically, it would be possible to find > one, a *formula* would be of no use. That is why no one is suggesting the > use of formulas. The reduction of our approaches to finding formulas is > another conceptual bias of yours, not of ours. You have failed to recognize > that there are other ways to describe things with mathematics than mere > formulas, and so you see mathematics as insufficient to the task as a > result of that intellectual failure. >>Math is an extensible language for > patterns ("schema").<< > > I can't see that entire image, since I'm on my phone, but in what I can > see of it, you have various closed loops, maybe with other closed loops > inside them that don't touch the outer ones. These could be thought of as > outlines of shapes. So the common schema, in mathematical terms, is "an > enclosed area with countable areas inside it that have been excluded". > Thus, we have (1) an outer boundary, which is a loop, a continuous path > which can be described to any level of approximation by a sequence of > points, as is done by the very image format which allowed you to present > these blobs to the group in the first place, and (2) zero or more inner > boundaries, also described by loops, with the restriction that they are > inside the outer loop, and none of the loops touch each other. (They don't > have any points in common.) The definition of "inside" is probably the most > difficult to express in mathematics of the concepts required here. I would > refer you to any analytic geometry book for a *formal* definition of the > various concepts I've used. They have already been defined, and so the > shapes you gave are fairly straight forward to handle algorithmically. > > This schema (*not* a formula!!) is only one of many ways to capture the > commonalities of these shapes in mathematical form. Do I have to actually > *write* the algorithm for you to believe me? Or can I just open up Paint on > a Windows machine and use the "color fill" mechanism to demonstrate for you > an algorithm that's already been written? > > > > > -- Sent from my Palm Pre > > ------------------------------ > On Nov 6, 2012 3:57 AM, Mike Tintner <[email protected]> wrote: > > What’s amazing, Aaron, is that you guys – and it is general – have a > virtual cognitive deficit here - > > a complete inability to recognize that regular units are fundamentally > different from irregular units, and general (regular) units are > fundamentally different from individual (irregular) units – and that > science which depicts general classes and what they generally have in > common, is fundamentally different from the arts which depict individuals > and what makes each one different and distinctive. Generalizations about > “human beings” are fundamentally different from individual portraits of > “Hamlet” and “Falstaff” and “Holden Caulfield” and “the Mona Lisa.” > > You can’t boil down the one to the other – they are opposite and > **complementary**. But there is an absolutely mad egocentricity esp. in > this field, but also in the whole of science, that refuses to understand or > even look at the opposite position. > > Formally it comes down to this – and it is no abstract philosophical issue > – but the centre of AGI - > > there is no formula for : > > [image: blobs] > > There is no formula for a group of irregular units – there is only a > formula for a group of regular units. > > This is a simple truth. And y’all cannot either disprove it or deal with > it. > > The common mistake you all make over and over - and it’s painful – is to > say: “but I can reduce that shape there to a geometrical definition.” > > Yes, you can reduce ONE shape to a geometrical definition, but you can’t > reduce ALL of them – the whole group. > > But the human mind CAN reduce all the above irregular units to one common > SCHEMA of “blob[s]”. > > Not a common formula, but a COMMON SCHEMA. > > And that is the central unsolved problem of AGI.- to give machines that > capacity to **schematise diverse irregular units** – which is fundamental > too to creativity generally, not just object recognition and > conceptualisation. > > Frankly, this field may well be the most creatively unimaginative in the > history of technology. > > Faced with a major creative problem – *how does the brain schematise > irregular, diverse objects?” – all this field can do is to plug the same > old technologies over and over – and just utterly refuse to think of > anything new. Which is simply WRONG – it never has worked or will work. > > You are all esp trying to plug maths when it is failing utterly in terms > of AGI - > > all trying to think inside the same old boxes. > > Well, this is both literally and creatively, an area where the solution > lies in thinking outside the [geometric] box. Moving into a whole new > formal field. > > One way or another, you will never find a formula for those > blobs/islands/cells above. And I can present the same old problem in > different guises to you over and over, and you will all always run away > from it. > > I’ve also presented the solution to you – at a philosophical level. And > that level is translatable into mechanical terms. > > > > > > > *From:* Aaron Hosford <[email protected]> > *Sent:* Tuesday, November 06, 2012 4:38 AM > *To:* AGI <[email protected]> > *Subject:* [agi] Randomness: Mathematics as Perceptual Bias > > Mike, here's something for you to chew on: > > I like to think of the term "random" as meaning the absence of a * > detectable* pattern, due to biases and/or blind spots of the observer or > perspective. Under this definition, it is implicit that anything can be > seen as random or non-random given an appropriate observer or perspective. > > I think our minds are simply filters for reality, designed to pluck out > the most common and useful patterns through appropriate biases. We look for > the patterns we do because they help us accomplish our evolutionary > purpose. When something looks random to us, it simply means we can't > identify a pattern, not that there isn't one. > > Mathematics is a language for representing the sort of patterns the human > mind tends to perceive. It is, in other words, a language for representing > reality in terms of our intrinsic human perceptual biases. We have integer > arithmetic because we perceive discrete, countable units in the universe. > We have calculus because we perceive continuous phenomena such as curves, > areas, volumes, and flows in the universe. We have geometry and topology > because we perceive shapes and invariances of shape in the universe. We > have logic because we perceive a mapping between situations and their > descriptions (language, including math) in the universe. And we find > commonalities and relationships between the various branches of > mathematics, described in the terms of logic because logic is the language > we use to talk about languages, including those of mathematics. > > Much of the confusion and failure generated by Boolean logic, the most > commonly used and least versatile form of "fully functional" logic, arises > from the failure of Boolean logic to recognize the distinction between > different kinds of false statements (pieces of language). Boolean logic > only recognizes statements that are false because their opposites are true. > But it completely disregards the existence of statements which cannot be > mapped to reality to verify their truth. These sorts of statements are not > false because their opposites are true, but because they are meaningless. > This lack of distinction (a bias towards perceiving truth and falsehood but > not meaninglessness) is the source of many mathematical and logical > paradoxes. > > As for your "irregular forms", Mike, what all this boils down to is that > if the regularity of some aspect of the world isn't visible to mathematics, > it isn't visible to *people*. Mathematics simply codifies what our brains > already do. When we notice a regularity in reality, we create a branch of > mathematics to describe it. If we don't see a regularity in a portion of > reality, we call it random and mentally disregard it. I am identifying > concepts themselves as human-perceivable regularities in the world, in case > that isn't readily apparent. Thus if we can conceptualize something, it > must be regular in our minds, and either a branch of mathematics exists to > describe those regularities, or we can create one. (These new branches of > math always start out as human language and become steadily more formalized > as we become more certain about what the regularities are and how to more > effectively describe them in language.) > > So, in summary: > 1) A concept is a human-perceivable regularity. > 2) Mathematics is a highly refined language for describing > human-perceivable regularities. > Therefore: > 3) Mathematics is a highly refined language for describing concepts. > > Mathematics (and language in general) is how we tell each other about the > world. If something can't be described in terms of mathematics, it's > because it either can't be perceived, or we have identified a new branch of > mathematics that needs to be created. Eventually, we will have covered all > the filtering biases evolution has built into our minds, and mathematics > will be sufficient to describe all concepts the human mind can perceive > without further additions to the language. > > > > > > > > *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/303/23050605-bcb45fb4> | > 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/303/23050605-bcb45fb4> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <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-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
