I feel in this, Frank, like your comments will fall on deaf ears, for an interesting reason. The thing you summarize for Nick is precisely the thing he wants to object to.
It seems to me that Nick believes that Zeno’s arrow paradox, https://plato.stanford.edu/entries/paradox-zeno/ <https://plato.stanford.edu/entries/paradox-zeno/> or something close to it, defines in some Platonic way the “right rules of thought”. Whatever Zeno’s rules of argument make ill-defined, we should somehow believe isn’t really properly conceived, and _cannot be_. If I were to tell Nick (replace “momentum” where he has “acceleration” in the sentences below), that in 1833, Hamilton took us beyond all the things Zeno can’t do, by writing the states of objects in a 2-coordinate space, where one coordinate is position and the other is momentum, and the two coordinates are _independent of one another_, and in some important sense _symmetric_ and _peer_ attributes of the object, I would not be addressing his objection to calculus (which does define these things in limits as you say below), but I would be arguing that physics may suggest the limit-definition from calculus is not the most fundamental one. If I were then to tell Nick that the duality between being at a place (all position) and being in a state of motion (all momentum) became in quantum mechanics the duality between standing and traveling waves, and that we understand their independence and peer status even more thoroughly in quantum mechanics than in Hamilton’s classical mechanics, I would still not be addressing the unquiet about calculus, but would perhaps be asserting that physical reality is even further from needing its in-the-limit definitions. But the part of this that is interesting (to me) is: why is this Nick-as-I-perceive-him (which the real Nick may or may not be) convinced that Zeno’s rules of argument are somehow the defined “right rules of thought”? Why is anyone convinced that he knows ahead of time what rules are the right rules of thought for anything? Why are we not somehow always aware that all these words and rules come up together somehow as parts of a mutually-interdependent system, really “pulled up by their own bootstraps” in a much more perfect way than the way that metaphor is used for the startup of an operating system in a computer? And if we were thus aware of the somehow out-of-nowhere character of the bootstrapped systems within which all the terms and rules take their meaning, how would it then change the way we think about choosing which one to use? The Platonists in their own words b believe that truth somehow comes to them through the divine channel of thought from a reality beyond experience. I think they are more fond (in the original sense of “crazy”) of their own preconceived notions than they are of the complexity of experience, and mistake their preconceived notions for a more ultimate and perfect, but in any case preferable “reality”. If we get out of that habit, how does our style of argument for what constitutes right thought change? Neither here nor there to this thread, I did want to mention some weeks ago that I really liked Glen’s formulation of The Will to Simulation. I think Nietzsche would have appreciated its irreverence, though he would have been too vain and obstreperous to contribute anything to it. Eric p.s. On the above, I could have stayed with Nick’s original query about acceleration, and gone to physics. I could have spoken of his very physical self, standing here on the surface of the Earth, and accelerated away from the world-line of an inertial observer in general relativity by the fact that the Earth is in the way of his free fall. The gravity that he feels in the seat of his pants is the acceleration that is a property of his state. But it was simpler to refer to momentum and to go back to Hamiltonian mechanics, which has an additional century behind it, and which really marked the turn away from Zeno and a definition of velocities in terms of derivatives by Lagrange, and toward a recognition of momentum as an inherent property. If one can see that clearly and with familiarity, it is then a straightforward next step to say that Mach’s principle just said “if frame-independence applies to velocity, then why not also to rotational velocity, and what then do we do about acceleration”, and you get the case from general relativity. > On Oct 1, 2021, at 10:00 PM, Frank Wimberly <wimber...@gmail.com> wrote: > > Nick, i hope this helps. Given a fair die that hasn't been thrown the > probability that it will come up 2 (or any of the other particular values) on > the next throw is 1/6 by definition of fair. Given that it has been thrown > and ceterus paribus the a posteriori probability that it shows 2 given that > it does is 1.0. In that case the probabilities of each of the other values > is 0.0. > > The acceleration of an object with constant velocity is 0.0. If the velocity > is changing the acceleration is the instantaneous change in velocity the > knowledge of which is limited by the ability to measure that. The > acceleration of an object whose velocity is described by a closed form > mathematical function is the derivative of that function as we learned in > calculus. The derivative is defined by limits. This is theoretical and > approximates what happens in the physical world. > > Questions and comments are welcome. > > Frank > > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Fri, Oct 1, 2021, 7:21 PM <thompnicks...@gmail.com > <mailto:thompnicks...@gmail.com>> wrote: > I thought the conversation about probability, category errors, and crossing > boundaries between levels of organization was interesting and I was sorry I > had to leave it. I want to say that to speak a die as having a probability > of 1/6 of coming up 6 on a single throw is a category error because it is not > a property that can be displayed on a single throw. It’s the same worry that > I have often deployed about the calculus. If we take the idea of a category > error seriously, then acceleration is just not the sort of thing an object > can have at an instant. But just as clearly as this argument is too strong > – lots of very nice longstanding bridges have been built with the calculus – > so the argument is also too strong with respect to probability – lots of nice > atom bombs have been built with probability theory … or something. > > > > I care about this because my standard account of such concepts as “wanting” > is that they are properties of the population of responses to an object, not > properties of any one of those responses. We encounter the same problem > with anecdotes and newspaper photographs designed to illustrate some general > fact. If the generally fact is that “very few of the immigrants at the > southern border are well treated” a single photograph looking peaked or > hungry is irrelevant. Equally irrelevant would be a picture of a bright eyed > kid sitting in the lap of a border patrol officer eating a hot-fudge sundae. > > > > This makes me wonder about one of the foundations of psychological research, > the statistics of inference, which I think Peirce invented. Let a coin be > thrown 10 times and each time come up heads. What I think Peirce would have > me conclude is that that coin is unlikely to be drawn from a population of > fair throws of a fair coin. But, of coure, what we are likely to conclude > is that “this coin is not fair.” But that could be as misguided, couldn’t > it, as concluding that the kid in the lap of the border patrol officers is > being mistreated. > > > > I apologize, once more, for sharing my comfusions with you. > > > > n > > > > Nick Thompson > > thompnicks...@gmail.com <mailto:thompnicks...@gmail.com> > https://wordpress.clarku.edu/nthompson/ > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f&c=E,1,QU0qVpqNOoJiPM24Dv11INL-P7InBOIA4z4LOnpttneeWXYwPuFzZKWaVU3KPxC8ObCG7JECy2fbQeuL-V9-2OsvQN3I7mXpu9mzsoPaIE0,&typo=1> > > > From: Friam <friam-boun...@redfish.com <mailto:friam-boun...@redfish.com>> On > Behalf Of Frank Wimberly > Sent: Friday, October 1, 2021 6:46 PM > To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com > <mailto:friam@redfish.com>> > Subject: [FRIAM] Newborn Heart Rate > > > > > https://pediatrics.aappublications.org/content/61/1/119 > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fpediatrics.aappublications.org%2fcontent%2f61%2f1%2f119&c=E,1,uD1tIhc7c-0wZqgMnI5_Ki1-cJ9QDa1EyaSQIuM5xQO8giKGtKM8z1rtfEnJ33KUkPyECbG92OSX1Pt-uIL6rgVLiylCxIbiMASMUnV7SEjwSw,,&typo=1> > > > This is for those who attended this morning's vFriam meeting. I was > Schachter's colleague, among a couple of others. > > > > > > --- > Frank C. 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