Thus spake Ted Carmichael circa 11/02/2009 11:59 PM: > Yes; I will now call you "Glen the pedant." ;-)
That's not near good enough, since I'm poorly educated and an anti-intellectual... from Texas no less... You'd have to include something about hypocrisy or hubris, too... hypocritical hubristic pedant? [grin] OK. No nits this time. > > On Mon, Nov 2, 2009 at 8:07 PM, glen e. p. ropella < > [email protected]> wrote: >> >> Translating methods from one person to another involves scale to the >> extent that the scale chosen for observing is capable of precisely >> mapping measurements of the other guy's actions to controls for your >> own. As such, it's not arbitrary, at all. In some contexts, scale must >> be carefully chosen and in others scale is irrelevant. We can often >> translate methods from human to human because regardless of what scale >> is chosen, we are similar all the way up and down all the scales. > > > ?? I don't get this part. I'm 6'5", which means there is a ~99% chance I am > taller than you. As such, my jump shot will differ from yours in many > subtle ways. I disagree. The actions can be the same. The states are necessarily different. The actions will scale (i.e. be invariant to changes in scale) from my height to yours, primarily because we're working in a metric space. I.e. the state space is very well behaved. The method can be the same but a trace of either method will show different values in the same space. >> And >> this is also what allows us to trust the false concept of translating >> ideas from human to human, which was what my original criticism was >> about: Ideas should not be a part of this conversation of novelty. >> > > You have to prove that, I think. Occam's razor and all. The > null-hypothesis would be that similar ideas spring from similar mental > processes. Oh no, no, no, no. In order to apply a principle of parsimony for a _theory_, we need the theory. And "idea" is an ill-defined (actually undefined) construct. So, if you include "idea" at all, you've already thrown Occam out the window. We can't measure ideas. We can't point to ideas. We can't ship them around the country via UPS. Etc. Ideas are ephemeral and, I argue, fictitious. Theories (especially testable ones) don't include ideas at all. Theories involve sentences, statements, rhetoric, etc., but not ideas. Going back to Crutchfield, this is part of what he's recognizing. The 4 types of mechanics he talks about are not about ideas at all. They are about descriptions, languages, model classes, real stuff outside the mind. >> OK. I don't think methods can be tacitly distinguished by choice of >> scale. To be clear, measurements (state) can be distinguished by choice >> of scale; but actions (functions, methods) can't. So, if we choose the >> coarsest scale for the basketball example, we have two states: 1) ball >> at point A and 2) ball in hoop. At that scale, you're right that you >> can't distinguish the measurements from the jump, hook, or granny shots. >> Then add more states, let's say: 1) ball at point A, 2) ball at point >> B, and 3) ball in hoop. Between the 3 methods, state (2) will be >> different. So, again, you're right that you can distinguish the TRACE >> of the methods. >> >> And you can then argue (by the duality of congruence and bisimilarity) >> that a distinction between the measurements implies a distinction >> between the methods. But you can't distinguish between methods directly. >> > > I'm not sure what you are getting at here. If you can watch someone playing > basketball, and you know when to say "That was a jump shot" and when to say > "That was a hook shot," then you are able to distinguish between the > methods. If you aren't able to see the difference, then you are probably > using the wrong scale for your analysis. Sorry if I've been vague. I'm saying that you cannot measure the processes. You can only measure the results of the processes, the states of the system. For example, let's say we have a machine with states A, B, and C and transition functions f, g, and h such that f(a in A) = b in B, g(b in B) = c in C, and h(c in C) = a in A. You cannot measure f, g, and h, the functions, the methods. You can only measure the states a, b, and c. So, when you watch someone play basketball and you _measure_ one player's approach to the net and attempt to put the ball through the net, you're not observing the actions, the functions, the method(s), you're observing the various states of the system (at a very high sampling rate). The point being that there are states through which the system travels that you cannot observe, even at that high sampling rate. And, most importantly, you can NEVER directly observe the actions, functions, methods whose results are the states you do observe. You need a hypothetical construct like the duality between congruence between states and bisimilarity between actions in order to conclude that your observation of the states is good enough. That's what I'm saying... [grin] Of course, you may well ask why I'm saying that... to which I'd reply: because the transferability of methods from one particular to another particular depends fundamentally on the bisimilarity of the two machines, not the sampling rate at which the measurements are taken. > When you say two different > methods are capable of producing the same trace, then your scale is very > coarse and limited ... you're only using 2 or 3 states of where the ball is. > Which is fine, if that's how you chose to analyze the action. But given > that scale, the *similarity *between the two people that produce the trace > doesn't matter. You're not even looking at the people. (Inferred by the > fact that you don't care to differentiate between the methods.) I'm saying something much stronger. Methods are transferable when the source machine and the target machine are bisimilar, i.e. their transition functions (actions, movements, processes, not state) are the same. And we cannot measure transition functions, no matter what the scale or granularity or sampling frequency. Now, to the degree we can fill in the blanks when we see the trace of some other machine's actions, then we can reconstruct a congruent trace with our own machine. But that reconstruction is made more difficult if the other machine is very much different from our own. Sampling frequency (aka scale) does matter. But it's orthogonal. What really matters is the ability to fill in the blanks. And that is governed by the similarity between the functions of the two machines. I hope that's clearer. > Is that how he defined innovation? That the new model class is necessarily > more expressive? If so, I missed it. I thought he just said innovation is > jump to a *different *model class. Well, there is an _implication_ (Nick's right that Crutchfield is ambiguous) that the modeler changes model classes because the previous one is somehow inadequate and the new one captures the referent better. That doesn't necessarily imply a superset of expressive power. But it's damn close. Movement to a more expressive model class will always be innovative by this measure. But a kind of "lateral" movement where the new language is equally expressive but a better natural fit to the referent would probably also qualify. Perhaps even a "downward" movement to a class that is less powerful might be innovative in the sense that _if_ you can use a less powerful (and hence less complicated) class to adequately represent the referent, then that's a good thing. But, really, if the less expressive class can represent the referent efficiently, then so can the more expressive class. All that would be required is a different model within the same class. So, I suspect Crutchfield would require at least "lateral" movement in the model class hierarchy, if not "upward" movement. >> By analogy, imagine a 2 dimensional real (pun intended) plane. We >> already know of all the functions like x^2, x^3, x+y, etc. Then when I >> take my pencil and draw some squiggly line across the plane, is my new >> "function" really new? >> > > Yes! That's the beauty of it. The elements are already defined, and the > number and type of squiggly lines are limited by these elements. But your > line is (presumably) a new combination of these elements never seen before. > Just like Windows 7 is a new OS, combining 1's and 0's, and using logical > NAND gates, in a new way. I just have to flatly disagree. I don't think arbitrary new squiggles on a 2D real plane or Windows 7 are novel according to Crutchfield's criteria in this paper. The model class hasn't changed. The squiggly line is just like any other curve and Windows 7 is just like any other of our present operating systems. (Now, one might argue that Plan 9 or the Hurd are novel, because -- according to my ignorant understanding -- they are fundamentally different than their brethren; but not Windows 7. Ugh! Why are we talking about a microsoft product? ;-) -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com -- 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
