I'm actually fine with re-defining 'scale' to mean something along the lines of the amount of error in the mapping. That is mostly, I think, what I was trying to say. Let me see if I can clarify my points a little.
There is definitely a large number of differences between two people using the same method to shoot a basket. All the things you mentioned - eye movement, exact combination of muscles, etc. I was trying to say that this is a different scale (a wider range of error, perhaps) when compared to two shooters using different methods ... e.g., one person shoots in the traditional way and one person makes a 'granny shot.' I agree that two people using the same method is an illusion. But it is a useful illusion, when differentiating between the traditional method and the granny method. Similarly, when Kareem Abdul-Jabbar used the hook shot, it was an innovative (hence: new) method for the NBA. In this way I would say there are different levels of abstraction available ... one simply picks the level of abstraction that is useful for analysis. I tried to use the mathematical example of calculating a product to illustrate this same idea. When calculating 49 * 12, one might use the common method of using first the one's column, then the ten's column, and adding the results, etc. Another person may invent a new method, noticing that 49 is one less than 50, and that half of 12 is 6, and say the answer is 600 - (12 * 1) = 588. Still another may say that 490 + 100 - 2 is the answer. What is innovative about these new methods is not that they ignore the common operations of adding, multiplying, and subtracting. It's that these basic operations are combined in an innovative way. If Crutchfield asks: is this really something new? I would say "yes." If he points out that all three methods use the same old operations, I would say that doesn't matter ... those operations are used in an innovative way; in a new combination. In a slightly different vein, Java is a "new" programming language even if it is only used to implement the same old algorithms. The implementation is new, even if the algorithm - the method - is the same. This is analogous to two mathematicians using the same "trick" to get a product, even if the respective neuron networks each person possesses to implement this method are slightly different. I do admit the term "level" or "scope" can exhibit ambiguities. But I still find that "level" is a useful distinction. It does imply varying degrees of complexity, and I think that is a valid implication, even if it is hard to nail down. I also find it hard to define a counter-example to the proposition that emergent features of a system are always produced from the interactions of elements "one level down." When we look at a marketplace, we assume the "invisible hand" is the result of human interaction. There doesn't seem to be much use in jumping from the level of neurons - or even worse, quarks - straight to the marketplace. Of course, depending on the scope of the "market" being studied, individual businesses and other multi-person entities may be the most basic element of this system. There may even be entities defined as "one person" within this system, depending on how much heterogeneity you allow between individual elements. But, however you define the elements, this essentially means the same as saying "one level down," when talking about the emergent properties of that system. If you want to talk about the emergent properties of a corporation, then you have redefined your system, and hence redefined your elements. Anyway, the larger point is that innovation happens by combining elements in a new way, however those elements are defined. A RISK processor is innovative in how it combines basic computer operations. Java is innovative in the instructions sent to the processor, and the package of common tools that comes with it. A new algorithm is innovative in how it uses these tools at a different level of abstraction. And a software package may be new in how it combines many existing algorithms and other elements of visualization and human-computer interaction. If you don't like "levels" and prefer "layers," then I'm okay with that. But I don't really see the distinction. Can you expand on that? Cheers, Ted On Sun, Nov 1, 2009 at 11:43 AM, glen e. p. ropella < [email protected]> wrote: > Thus spake Ted Carmichael circa 10/30/2009 03:33 PM: > > In response to Glen's comments, I would say that his differentiation > between > > thoughts and actions is also a somewhat arbitrary choice of scale. I > agree > > that how two people shoot a basketball is usually more easily translated > > between them than how they calculate the product of two numbers. When I > > shoot a basketball, I follow the same general procedure (knees bent, one > > hand on the side of the ball and one hand behind it, etc) that other > people > > do. But my physical structure is still different than another person's, > so > > I have refined the general procedure to better match my physical > structure. > > (Or not, since I usually miss the basket.) > > Yes, you're onto something, here. But I wouldn't consider it a matter > of general vs. specific for throwing a basketball. Any general method > you may think exists is an illusion. Let's say you're learning how to > do it from a coach and several fellow players. For each other person > you watch do it, their method is particular to _them_. In such a case, > there is no general method. You may _imagine_ some illusory general > method in your head. But when the method is executed, it is always > particular. > > Now consider the coach's _description_ or model of the method. Even in > that case, the description, the words, the actions the coach executes > with his mouth and hands in an attempt to communicate an idea are > particular to him. The descriptive actions are particular to him. Even > in that case, there is no general method. Any general method you may > think exists is pure fiction. What matters is the particular actions. > > Induction is a myth. [*] > > It's not general vs. specific. It is abstract vs. concrete. You're > observation of either the coach's description or your fellow players' > methods is chock full of errors and noise. In order to cope with such > noise and translate from their actions to your actions, you have to fill > in the blanks. You are totally ignorant of, say, how fast to twitch > your eyes while you're maintaining focus on the basket... or how fast to > twitch your hand/finger muscles while holding the ball. You can't > observe those parts of the method when watching your fellow players. > And such information is totally absent from the coach's description. > So, you have to make that stuff up yourself. > > And you make it up based on your _particular_ concrete ontogenetic > history. And, hence, when you execute the method, it is also particular > to you. > > However, because your hands, fingers, and eye muscles are almost > identical to those of your fellow players and your coach, the method is > transferable despite the huge HUGE _HUGE_ number of errors and amount of > noise in your observations. > > > Two different people calculating a product, however, may use two totally > > different methods. One person may even have a larger grammar for this, > > utilizing more methods for more types of numbers than the second person. > > (In effect, he has more of his brain dedicated to these types of tasks, > > which give him the power to have a larger "math" grammar.) So it's > probably > > more precise to say: at a certain scale 'actions' can be mapped between > two > > people but 'thoughts' cannot be. > > It's less a matter of scale than it is of noise and error. When > calculating a product (or doing any of the more _mechanical_ -- what > used to be called "effective" -- methods), the amount of noise and error > in the transmission from one to another is minimized to a huge extent. > Math is transferable from person to person for precisely this reason. > It is _formal_, syntactic. Every effort of every mathematician goes > toward making math exact, precise, and unambiguous. > > So, my argument is that you may _think_ that you have different methods > for calculating any product, and indeed, they may be slightly different. > But the amount of variance between, say, two people adding 1+1 and two > people throwing a basketball is huge, HUGE, _HUGE_. [grin] OK. I'll > stop that. Because (some) math is crisp, it's easier to fill in the > blanks after watching someone do it. > > Now, contrast arithmetic with, for example, coinductive proofs. While > it's very easy to watch a fellow mathematician add numbers and then go > add numbers yourself. It's quite difficult to demonstrate the existence > of a corecursive set after watching another person do it. (At least in > my own personal math-challenged context, it's difficult. ;-) You can't > just quickly fill in the blanks unless you have a lot... and I mean a > LOT of mathematical experience lying about in your ontogenic history. > Typically, you have to reduce the error and noise by lots of back and > forth... "What did you do there?" ... "Why did you do that?" ... "What's > that mean?" Etc. > > Hence, it's not a matter of scale. It's a matter of the amount of > error, noise, and ignorance in the observation of the method. And it's > not about the transfer of the fictitious flying spaghetti monsters in > your head. It's a matter of transferring the actions, whatever the > symbols may mean. > > > If you go down to the lower level processes, all of our neurons behave in > > approximately the same ways. So at this scale they can be mapped, one > > person to another. I.e., when thinking, one of my neurons is just as > easily > > mapped to one of your neurons as my actions are to your similar actions. > > Right. But similarity at various scales is only relevant because it > helps determine the amount of error, noise, variance, and uncertainty at > whatever layer the abstraction (abstracted from the concrete) occurs. > Note I said "layer", not "level". The whole concept of levels is a red > herring and should be totally PURGED from the conversation of emergence, > in my not so humble opinion. ;-) > > > * I have what I think are strong arguments _against_ the position I'm > taking, here. But I'm trying to present the argument in a pure form so > that it's clear. I'm sure at some point in the future when I finally > get a chance to pull out those arguments, someone will accuse me of > contradicting myself. [sigh] > > -- > glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org >
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