John: Math itself is a great example of “Iconic Programing” and vice versa
Well, you’re half right – in that if you analyse carefully the whole system of reasoning, (wh incl. the human operator and not just the computer), then everything incl. maths and logic and all symbolic systems) is imagistic. And, yes, you can, strictly, classify maths – geometry – as icons. And that is consistent with my classifying maths as one half (the more important half – inasmuch as it provides the structures) of an Abstract Formal Science. However, the point I’m making – wh. no one has directly addressed or discussed – is that maths involves a particular kind of icon, not all - consists of **fixed, regular icons [/forms] ** and *fixed regular transformations.** “Perfect** forms and transformations. That enables maths to be formulaic – which is the foundation of maths. What maths does not and cannot deal with is the **fluid, irregular icons/forms** and **fluid irregular transformations** of the vast field of **cultural icons**. One of the new and v. important ideas I just put forward is that: “hey here is this vast field of cultural icons.” From the icons on your computer desktop to the icons of traffic and public signs to the icons of logos and advertising to the icons of diagrams and the vast area of diagrammatic/”neo-flowchart” thinking These icons are real visible – absolute facts of cultural life and they are myriad and permeate our life – especially with a sort of “titular” function. There may well be somewhat as extensive an “iconic objection” as there is “verbal lexicon.” Distinguish them from the fluid schemas that I and to some extent Lakoff & co have been talking about – these are *theoretical* constructs about what I/we imagine to go on in the brain. Cultural icons are v. v. real and open to the same formal analysis as geometrical “icons” – and that we can understand them, provides very strong empirical evidence of how the brain works.. And these icons demonstrate empirically that 1) they do NOT bear any geometric relationships to their subjects. No fixed, formal, formulaic relationship. Icons of all subjects from “man” and “woman” to “hill”, “car” and “dish” or “[swimmer] swimming”. - their relationship is fluid, informal, truly iconic/ideal vs formulaic, multiform rather than uniform . One icon can clearly embrace many diverse forms – a “man” or “face” icon can embrace “squarish,” “triangularish”, “circular”, AND “pearish” forms. There is nothing in maths that can do this. There is demonstrably, no mathematical formula that can simultaneously generate square, triangle, circle, ellipse and rectangle forms. Maths is not meant to do this. This provides a clear delimitation of maths. 2) Icons themselves are fluid and multiform. You can have a never-ending set of vastly formally diverse icons for the **same** object. Stick, arrow and circle, rectangular and curved limb forms can and do ALL represent “man”. This is very powerful evidence that the brain’s own “icons/schemas are fluid and multiform – the brain (as I have insisted) does not need consistent “prototypes” of objects. It can and does work with fluid, everchanging prototypes/icons/schemas. [N.b. If you want a demonstration of how revolutionary a thought this is – think of Plato’s Ideas. He thought – and in many ways science and maths still think – that the world and its objects are formed by consistent geometric “Ideas” – ideal,**consistent** forms of objects. No, this says, the generative forms underlying the objects of the world can be MULTIFORM, FLUID. God is not a rigid bugger - "God is fluid first – and, you might, say, rigid, geometrical second. God is artist AND mathematician.] 3)The icons of geometry and informal culture are distinct, OPPOSITE and complementary. Geometry provides the structures by which our culture views the world – the grids and ideal forms with which we analyse and compare the irregular multiform objects of the real world. http://www.iainclaridge.co.uk/blog/wp-content/uploads/0809/buddha_grid2.jpg Geometry provides the structure –you could say – but it is not “the Buddha” – or not the Buddha all by itself. Geometry is not either normal iconic or artistic drawing. And that clearly again culturally demonstrably, is how maths actually functions. Mathematicians are not artists. Maths and arts, demonstrably throughout our culture, are separate functions. You want to make it EVERYTHING - geometry to be ALL FORMS OF CULTURAL REPRESENTATION. It demonstrably is not. That is overweaning – and absurd in the face of geometry’s total failure to produce any AGI object recognition or conceptualisation. And the icons of our culture clearly demonstrate all this. P.S. I don’t want to get into a discussion again about this – unless s.o. wants to try and deal with the central challenge of AGI - how can a geometric formula/algo be truly iconic and generate square, triangle, circle, ellipse AND pear? But since you came back to the subject, I thought it was worth outlining this vast empirical field of icons – iconic representation. PPS You missed my other point – “iconic programming” requires a body – is a variation on the existing field of robotics (whose name I’ve forgotten – “morphogenetic”?) – where the body is used as a part of computation. Maths is definitely not embodied – it is artificial and abstract and non-physical in essence. And that too provides a massive delimitation of maths. [Give it up John Stop being a Platonic Luddite – try some of the revolutionary new ideas that are exploding around you] From: John G. Rose Sent: Wednesday, January 09, 2013 9:18 AM To: AGI Subject: RE: [agi] Why Logic & Maths Have Sweet FA to do with Real world reasoning Math itself is a great example of “Iconic Programing” and vice versa. Remember, math is instanced in a symbol set. Typically the most readily available is used. Others can be used to where math expands out using other symbol sets, different bases, etc.. You can even expand the symbol set out to where math doesn’t appear as math anymore and you can call it something different if one so desires J John From: Mike Tintner [mailto:[email protected]] What’s the point of this except to avoid having to think about a new idea? If an “iconic program” used logic and/or maths, they would only be parts, not the whole program. The point of doing AGI is to solve the unsolved problems by identifying new technologies – not to use old technologies that show no signs of working. Your loyalty is to the old technologies. Old technologies never solve new creative technology problems. That’s just a wrong idea. We didn’t get to jets by adapting the propellor, or to neural nets by adjusting linear programs. From: Ben Goertzel Sent: Sunday, January 06, 2013 1:27 AM To: AGI Subject: Re: [agi] Why Logic & Maths Have Sweet FA to do with Real world reasoning But if the robot is controlled by a computer program, that program is still embodying some logico-mathematical formula, at any particular point in time... -- Ben G On Sat, Jan 5, 2013 at 8:01 PM, Mike Tintner <[email protected]> wrote: P.S. What I should have spelled out is that the moment you connect an icon to a body - for example, an icon of a hand to a physical hand **the icon automatically becomes a fluid schema** because a hand – like the body - is in effect a fluid schema itself. What can an agent do with a hand? Nobody can state a definite bounded set or frame of hand movements. A hand is capable of virtually infinite hand movements.A fluid range of movements with many yet to be discovered and many continually being invented. So a hand icon [when connected to a body/hand] ipso facto refers to a potentially infinite range of hand movements/shapes etc. No one shall enter into the kingdom of AGI who is not a roboticist. AGI | Archives | Modify Your Subscription -- Ben Goertzel, PhD http://goertzel.org "My humanity is a constant self-overcoming" -- Friedrich Nietzsche AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription ------------------------------------------- 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
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