Robert, Just curious, I was very delighted to get your question, and thought I gave a meaty answer, but it apparently didn't connect. Rereading your question, though, maybe it seemed I was off on a tangent, since I didn't directly answer what you actually asked. Let me try again, and let me know if I'm still off the mark.
You asked about the term 'scale violations' and 'attributes whose derivatives are all positive' when things are born. By 'scale violations' I mean places in tracing the origins of things where you have to change your model of description because it's changes in kind violate your model. That happens at least four times for an individual: 1)starting from tracing your growth back from a youth to a fetus it's mostly the maturation of an established system, 2)before that the model has to change to describe the differentiation of the cells, and 3)before that has to change to describe the undifferentiated doubling of the single cell and 4)before that to describe fertilization, which also has precedents, but 5)they get lost in the complexity of the egg's inner world it seems to me. In the birth of a corporation it's similar, as the seed you can trace it all back to evolves through a succession of growth stages in which it becomes a whole different kind of organization and you need different models to describe it. I don't think 'attributes' actually ever change so that all derivatives are positive. I have a careful way of using that idea. In this case I had qualified it by saying 'have periods of' and 'implied derivatives'. Things that begin and end only have any property for finite periods, and strings of dots, as you know, don't have any level of derivatives unless you imagine some connection between them. Where the implication that things beginning from scratch have to display implied derivatives of the same sign comes from is a corollary of the conservation laws. Combining energy and momentum conservation and the limiting speed of light implies that infinite accelerations can't occur, consequently any beginning must develop. That is indeed what you observe in nature. What we can observe beginning does almost always do so with clear exponential-like growth curves, and things you can observe ending do so with clear exponential-like decays. That includes organisms and organizations. A smooth curve following those shapes will have all derivatives of the same sign. The actual rule I use is a topological interpretation of the corollary, that attributes of things that begin or end will have periods that trace a path between upper and lower bound exponentials. It seems like a loose requirement, but it works very well as a default assumption for identifying emerging systems with time series data. That's kind of technical, but I'm trying to give it a real bottom. You see any gaps? Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844 e-mail: [EMAIL PROTECTED] explorations: www.synapse9.com > Robert, > > On 10/15/06, Phil Henshaw <[EMAIL PROTECTED]> wrote: > > <snip> > > > >> It's very hard to tell when or if anything begins or ends, > >> because if so > >> it's at times and in ways that are too small to observe. > >> Another way > >> to say that is that beginning and ending always seem to > >> violate their > >> scales. That theorem I mentioned says that energy conservation > >> requires that if things are to begin or end they must do so > >> at invisible scales and have periods of development during > >> which all implied derivatives are of the same sign. The > >> testable part of that seems to > >> match observation. > > > > I need a couple of concrete example to understand this. Could > > you please tell me (i) the scale violations that occur and > > (ii) the attributes whose derivatives are all positive when: > > > > a human (me, for example) is born; and > > a company (Coca-Cola, for example) is born > > Robert > > Let me try, > > Not having any data for either event makes it harder to make > statements about how to interpret the data. Without data > everything is quite invisible, so let's talk about > hypothetical data. What might you choose?, the curvature of > your mom's belly, perhaps, and for Coke the documented assets > of the legal entity? You can quickly see that both might > make reasonably interesting measures of the early phases of > the development of either new entity, but are going to be > useless in locating "the beginning". > > Pregnancy develops a very noticeable curvature in a belly, > but tiny changes might be quite hard to measure accurately, > and a single cell, or probably even a million, won't produce > a noticeable change. The assets of a corporation are > problematic since it's beginning certainly comes before it's > a legally recognized entity. The formal signing of the > incorporation documents comes after lots of other organizing steps. > > One can work backward from the evidence you have, of course, > but it's all guess work and peters out. We can hypothesize > that fertilization is the beginning of a human, though it's > generally not observable, and then you can quibble about > whether it's the penetration of the cell wall or the > molecular joining that hypothetically divides before and > after, or another point. For Coke there might be a > particular handshake between two people to signify their > common commitment to form a corporation. It might even be > recorded at a particular time and place, but invariably it > will be the culmination of a process of idea sharing and > planning which is complex and perfectly untraceable as to its > beginning. > > You might try another tack. For each one try to find a time > prior to any evidence of their beginnings and work forward. > What you get is another fuzzy horizon, an greatest lower > bound to pair with your leas upper bound. If you liked you > could call the space between the forward and backward > approaches the definite period of beginning, but that's just > a window of probability, not the beginning. If it were just > a matter of always dividing time up finer and finer to make > it unclear when events that require a duration occur you > could agree to use some inflection point of a definitive > beginning moment or triggering event. That might be the > moment of the firmest pressure in the handshake or the signal > which the unfertilized egg sends to select which of the > pressing sperms is to be invited in. Events that fit that > convention might be found meaningful and useful in some > circumstances, but it's a convention to stop a search at a > satisfying point, not the result of finding their own > beginnings and ends. > > If you consider a single time-series data set, rather than a > ranging 'forensic' type investigation as implied above, > finding where the beginning of growth occurs is where the > horizontal line turns into a lasting upward curve. That's > inherently imprecise because the change one wishes to > identify is always smaller than the irregularity of the data. > > There's also the important question of whether anything > begins at all, or whether all things are unchanging and > ever-present in a universal continuum, and just emerging and > vanishing like the composite shapes produced by a Fourier > series. That seems plausible perhaps from a view that all > form follows mathematical functions. That's not anyone's > current view, I don't think, and becomes untenable when > watching how natural systems operate through resource pools. > Cells would need extra sensory perception to coordinate what > they deposit in the blood stream with what other cells > independently sweep up from the blood stream and make use of. > The weaker of two hypotheses is not a good candidate for > being one's automatic assumption and requires some > demonstration of feasibility to entertain. For things > existing in perpetuity there does not seem to be any. > Still, some things do definitely seem to happen, so they must > begin and end. > > I use the term "scale violation" to make it seem like there's > something remarkable about a trail of evidence vanishing into > the confusion of other contexts. Science has mainly focused > on questions where causation seems to be more definite. The > 'violation' is really of the common expectation that > definitive causes and evidence exist for everything and we > can potentially find them. I think when you carefully look > at beginnings and endings it looks like the opposite is the > case, at least for the point to point model of causation. > > As to finding periods of change having all higher derivative > rates of the same sign, that's the common feature of growth. > To treat data curves as having derivatives at all you need > the same thing you have for functions, a rule for finding > points along the curve that does not conflict with the > continuity of the underlying structure (physical or > mathematical). One slippery point is that you sometimes > can't demonstrate that the data at hand may be treated that > way (as having continuity). You might choose to first > assume it to be true, and then need to confirm that > assumption by being led to more substantial evidence from the > shapes you find. - This is basically about an investigative > tool, that leads to better descriptions, not a descriptive > tool itself. - Most times, though, any evidence of change > that begins and ends is enough to trigger the presumption > that there had to be a growth process of some kind to then go > look for, and treat the data accordingly... > > Of course, sometimes you just don't have the data. You could > say that not having evidence of a progression of change is > evidence of change without a progression, but you can usually > find more evidence of connecting progressions in proportion > to the effort you put in. Concluding that such evidence > does not exist would violate the conservation laws anyway and > call for confirming evidence of an absence. That amounts to > a proof by speculation based on a lack of evidence, and > that's usually unreliable. > > I would agree it may all seem a little sneaky, but it also > seems to work, so I don't mind. > > Phil > > > ============================================================ 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
