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Path: ...!weretis.net!feeder6.news.weretis.net!panix!usenet.blueworldhosting.com!diablo1.usenet.blueworldhosting.com!feeder.usenetexpress.com!tr3.iad1.usenetexpress.com!69.80.99.26.MISMATCH!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sat, 09 Mar 2024 19:36:00 +0000 Subject: Re: Acceleration's higher orders Newsgroups: sci.physics.relativity,sci.math References: <AricndPpR933M3f4nZ2dnZfqn_WdnZ2d@giganews.com> <ushsos$2caer$1@dont-email.me> <614f2594d8febab66c1ce843a1559e1d@www.novabbs.com> <v8WcnTTGsvcoMXH4nZ2dnZfqnPEAAAAA@giganews.com> From: Ross Finlayson <ross.a.finlayson@gmail.com> Date: Sat, 9 Mar 2024 11:36:05 -0800 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: <v8WcnTTGsvcoMXH4nZ2dnZfqnPEAAAAA@giganews.com> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit Message-ID: <hhOdnQGgD-m9J3H4nZ2dnZfqnPSdnZ2d@giganews.com> Lines: 145 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-dRzpsj+dO3IhwAcrAHKIqxBdCajB7zzmqyCd4wNKFk93nJOo2p0zqqgs9ISn9dh7dV/PvEzTzgHsJcq!CVTM8lkwv+u+HTCNrgEEpn3wJ4IOHUbKxN5JBmkI3OKvdZw+v7TYbKbkqFhlq+U8a9T74ZSdRpQ= X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 7922 On 03/09/2024 10:38 AM, Ross Finlayson wrote: > On 03/09/2024 08:34 AM, gharnagel wrote: >> Volney wrote: >>> >>> Ross wrote: >>> > >>> > So I'm wondering about v', v'', v''', that being >>> > acceleration and its higher orders, out to v^prime-infty, >>> > that at an instant, help figure this out. >>> >>> For what it's worth, some higher derivatives have (somewhat whimsical) >>> names. The derivative of acceleration with respect to time is called >>> jerk, the derivative of jerk is called snap or jounce, the derivative >>> of snap is crackle, the derivative of crackle is pop. Someone was a >>> breakfast cereal fan. The highest derivative I know of that's actually >>> used is snap, when designing the transition of roads or railroads from >>> straight to a curve they try to minimize the 'snap' of a vehicle >>> following the transition segment. >> >> I'd heard of jerk. Many years ago, Norman Dean "invented" the Dean >> drive, >> a system of rotating masses with the center of rotation of the masses >> being moved at particular times in the rotation cycle. He showed that >> the >> weight of the assembly was decreased when running - on a bathroom scales. >> >> William O. Davis analyzed the system which was referred to by John W. >> Campbell, Jr. as "the fourth law of motion" - i.e., jerk. Davis and G. >> Harry Stine got together and tested the invention. They hung it from a >> wire and oriented it so the supposed thrust would be horizontal. There >> was no net thrust. The "weight loss" was due to nonlinearities in the >> bathroom scales because of the thumping around of the weights. > > These days that includes "pseudomomentum not dead again", > "McIntyre's arguments to be re-read and re-though, re-visited", > "rest-exchange momentum", "balleton", these kinds of things. > > SUSY not dead again, .... > > Of course anybody who sat physics class and remembers it and internalized the concepts, knows that "scales" and "balances" are two different things, and we measure "mass" with "balances". (These days scales vary quite a bit, ..., day to day.) Here the idea that non-linearity starts as an infinitesimal impulse and results linearity, and vice-versa, is very much represented in "Einstein's Bridge", the converse, while the forward case very much is that an infinitesimal change cascades down to dv/dt, and, about dt/dv. With "meters per second, or, seconds per meter", is that it's "meters per second, and, seconds per meter". So, how it's usually figured is that f = ma and then that it's always integrated, here with the idea that the fuller integration, is to result what are currently neglected terms, to analyze the contributions of the non-linear or neglected terms, so it results all the real analytical character, includes the infinite series. The infinite series most always starts at the big end. Yet, change starts at the little end. The usual idea of infinite, is that there is no end. So, it becomes usual to work up finitely many higher orders of acceleration, and result that there's a big end and a little end. (In Gulliver's Travels there's an account of that in two land, the inhabitants ate hard-boiled eggs. Eggs have two ends, a big end and a little end. In one land, the inhabitants started from the big end, in the other, the inhabitants started from the little end, that what is trivial to one who'd eat from either end, resulted a cultural divide to the point of conflict. These days this is reflected for example in the computer architecture of most-significant byte B or bit b, to least-significant, in terms of a bit-sequence representing an integer, with the 1's place being least-significant and higher places more-significant, reflecting writing the numbers in order according to the bits of the digit and the digits as moduli, MSB-to-LSB, LSB-to-MSB, and msb-to-lsb, and lsb-to-msb, the "Big-Endian" and "Little- Endian", with regards to read-out is easier Big-Endian, while addressal is easier or aligned, Little-Endian.) So here, the usual higher orders of acceleration are usually under-defined after the first order, acceleration itself, "instantaneous" or "constant", f = ma, what results that f is a linear vector, and over time is what results force applied and work done, and all usually with a notion that conservation is energy. Yet, we have the great classical exposition of Zeno, in which we can being to frame all things with respect to the dialectic, of rest and motion, and relative motion, and uniform motion. Here it's sort of the idea, that a cylinder is standing upright, only most-minimally locally stable, then a feather lands on it, and it tips, converting all of its potential energy in its oriented stable configuration, to kinetic energy, what with regards to reaching another, more, yet still locally, stable configuration, lieing down. So, the feather, is an infinitesimal, and it's the little end, of the cylinder's minimization of potential energy, just as an example of the sort of thing, that the cylinder is arbitrarily stable and the feather while arbitrarily small is arbitrarily large, with respect to the arbitrarily stable configuration of the cylinder, or obelisk, which is arbitrarily high, thin, narrow, or wide, keeping things simple in the configuration space, while general as these things are. Then, for Zeno, is this notion of, "meeting in the middle", "middle of nowhere", this is the sort of accompaniment to "21'st century Zeno", which not only models ancient Zeno, but every edition and each variation between. So, in physics, there's singularity theory. One of the usual most usual notions of applied physics, is that "singularity's don't exist", then, though, what results is "they do", then, furthermore, "singularities are multiplicities", vis-a-vis, "singularities are either origins or attractors". Then, for the infinite and being down at both ends, is much about, being around. (And through.) So, "acceleration's infinitely-many higher-orders", is a fundamental concept that reflects the very notion of state, configuration, and change, itself, and of course is what must follow from a very thorough and didactic deconstructive account of "Zeno: then and now".