"common elements" != "identical elements" Nobody ever said they had to be identical elements. The things you're counting are all >>things<<. That's the commonality they have. And that's all the commonality they're required to have in order to satisfy the requirements of counting, and therefore of the number 9 treated as a pattern.
In computer science, there is the concept of classes, which are types of things. They are defined striclty in terms of what their instances have in common. So we could have a class called Integer, and its instances would be 0, 1, 2, 3, -1, -2, -3, etc. Furthermore, we could define a new class, PositiveInteger, which is a subclass of Integer, meaning that every attribute of Integers applies to PositiveIntegers as well, or, identically, that every PositiveInteger instance is also an Integer instance. We can then define more complex classes whose instances are made up of combinations of other instances of other classes. For example, we could define a Coordinate class which consists of two Integer instances, one representing the x coordinate, and the other representing the y coordinate. We can then construct a Coordinate instance by putting together a PositiveInteger and a NegativeInteger, rather than just two Integers. Both the PositiveInteger instance and the NegativeInteger instance are themselves also Integer instances, but we have additional information about them because we know their subclasses. This additional information, however, does NOT make them no longer have their Integer-hood in common. Thus they are common elements, despite being non-identical, because we don't require identicality in common, merely general class or type. Thus, a complex class represents a pattern constructed out of common elements. These are not things that *could* exist, or that exist merely in theory or on paper. We organize the real-world flow of current inside the computer into these patterns, and we use them to control, predict, or even outright simulate things in the real world. We don't need to have identical things in the real world in order to computationally find patterns in them. They merely need to be similar, in some definable way. Computation can handle variety just as well as human brains can, because mathematics & logic let us define similarity and variety concretely and process them computationally just like anything else. On Fri, Aug 24, 2012 at 3:23 PM, Mike Tintner <[email protected]>wrote: > Look at the elements referred to by the concepts I listed – they are > *not* “common elements”. They can all be “diverse*/uncommon elements. > > Here, for example, are “7” poplars: > > > http://www.ibiblio.org/wm/paint/auth/monet/poplars-epte/monet.poplars-epte.jpg > > They do not classify as common elements. Each poplar is a different and > individual form. They do not form a pattern. > > Concepts create the “illusion” of referring to common elements/objects > (and therefore patterns) because of their apparent, *intrinsic* form - the > way they are spelled or numbered. > > C-H-A-I-R is always spelled the same way therefore surely there must be > an essential chair or chair pattern as Plato thought. > > “9” is always spelled/numbered the same way, therefore surely there must > be an essential number or pattern. > > (In fact, even that is an untrue illusion because all concepts can be > spelled and/or numbered with many diverse fonts!). > > To counter this, instead of an abstract “9”, try thinking in terms of a > graphic representation of the concept, such as “ l l l l l l l l l” - > (all concepts can and should be depicted graphically). > > Now it’s easier to see that while a concept may appear patterned > intrinsically, its REFERENTS are not. “Nine” or “seven” real poplar > trees will come in diverse, unpatterned forms, like those of Monet, not in > identically patterned lines like those of maths. Ditto nine or seven rocks, > snakes, apples etc. > > The real world referents of concepts and numbers don’t come in neatly > patterned forms let alone patterned groups. > > And each concept can refer to “all kinds of things” - all kinds of > poplars/trees, all kinds of chairs, rocks, streams, clouds etc. – which can > come in “all shapes, sizes and forms” not in uniform patterns.. > > Ben and Boris and you probably, don’t realise that concepts don’t refer > to a patterned real world, because you all live and breathe this artificial > logicomathematical world of perfectly patterned numbers and letters cut off > from the real world - at a metacognitive level, you never really apply > your concepts to the real world > > > > *From:* Aaron Hosford <[email protected]> > *Sent:* Friday, August 24, 2012 8:02 PM > *To:* AGI <[email protected]> > *Subject:* Re: [agi] Pattern: definition & incremental syntax.. P.S. > > "9" *is* the pattern. The rest of the details are parameters to that > pattern. I don't know if you program or not, but if you do, "9" would be a > class, and all the examples would be instances. You state the name of a > pattern, and then look at the context surrounding it and ask where it is. > You're subtracting out what you're looking for before you look for it, so > it's no wonder you can't see it. > > > On Fri, Aug 24, 2012 at 1:55 PM, Mike Tintner <[email protected]>wrote: > >> Those are really conceptual complexes. >> >> But it doesn't matter. >> >> Let's start with the obvious, "simple" concept of "9" . >> >> Which can refer to nine *abstract entities*, *trees*, *snakes*, *boxes* >> - >> >> or a "broken nine", or a "an inflated nine" or *nine diverse objects* >> or *a mixed-up nine* >> >> or * ......... * or " ^ /. h k < X ,@ " >> >> or >> >> Where's the pattern? >> >> [The same reasoning/examples applies to all the equations taken as >> wholes]. >> >> All the equations you cite, like the whole of maths and logic, are >> patterned, specific *applications*/examples of given concepts. >> >> But maths does not and cannot use concepts wholly/ properly with their >> open-ended realms of reference. >> >> Concepts like "Line" and "number" in ordinary language can embrace >> infinite examples, which are non-mathematical and which mathematics >> wouldn't go near. >> >> >> >> -----Original Message----- From: Matt Mahoney >> Sent: Friday, August 24, 2012 7:29 PM >> To: AGI >> Subject: Re: [agi] Pattern: definition & incremental syntax.. P.S. >> >> >> On Fri, Aug 24, 2012 at 2:19 PM, Mike Tintner <[email protected]> >> wrote: >> >>> show one single concept in the whole of *MATHEMATICS* or *LOGIC* that is >>> patterned. >>> >> >> 9 x 9 + 7 = 88 >> 98 x 9 + 6 = 888 >> 987 x 9 + 5 = 8888 >> 9876 x 9 + 4 = 88888 >> 98765 x 9 + 3 = 888888 >> 987654 x 9 + 2 = 8888888 >> 9876543 x 9 + 1 = 88888888 >> >> >> -- Matt Mahoney, [email protected] >> >> >> ------------------------------**------------- >> AGI >> Archives: >> https://www.listbox.com/**member/archive/303/=now<https://www.listbox.com/member/archive/303/=now> >> RSS Feed: https://www.listbox.com/**member/archive/rss/303/** >> 6952829-59a2eca5<https://www.listbox.com/member/archive/rss/303/6952829-59a2eca5> >> Modify Your Subscription: >> https://www.listbox.com/**member/?&;<https://www.listbox.com/member/?&;> >> >> Powered by Listbox: http://www.listbox.com >> >> >> ------------------------------**------------- >> AGI >> Archives: >> https://www.listbox.com/**member/archive/303/=now<https://www.listbox.com/member/archive/303/=now> >> RSS Feed: https://www.listbox.com/**member/archive/rss/303/** >> 23050605-bcb45fb4<https://www.listbox.com/member/archive/rss/303/23050605-bcb45fb4> >> Modify Your Subscription: https://www.listbox.com/**member/?&id_** >> secret=23050605-07077db3 <https://www.listbox.com/member/?&;> >> >> Powered by Listbox: 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
