Jon, Terry, list, I've seen it suggested in a thread somewhere on the Web that the reason that the position-velocity-acceleration trichotomy is a good one is that that there are universal laws of acceleration and velocity (and position?) but not of the third or higher derivatives. (The third derivative of position is informally known as jerk, also, jolt, surge, and lurch.) I don't know why there shouldn't be a universal law of jerk, becoming very salient when two strongly gravitating masses drift toward each other. But I'm no physicist. In fact, a two-ton truck does put on a few pounds as it moves from mountain top to sea level. The weight difference wouldn't make it fall faster, but I think that the difference in the strength of the gravitational field would. Otherwise one should be falling earthward at 32ft per sec. per sec. no matter how far from Earth one is. Also toward everything else in the universe. Then they'd all cancel each other out and there'd be no gravitation. I'd better stop before I drift too far out into space myself.
Best, Ben ----- Original Message ----- From: "Jon Awbrey" <[email protected]> To: <[email protected]> Sent: Thursday, March 22, 2012 4:56 PM Subject: Re: [peirce-l] C.S. Peirce • A Guess at the Riddle TB = Terry Bristol TB: I like it up to this statement that I find obscure. CSP: Now an acceleration, instead of being like a velocity a relation between two successive positions, is a relation between three; so that the new doctrine has consisted in the suitable introduction of the conception of Threeness. On this idea, the whole of modern physics is built. TB: I very much look forward to your comments on the overall passage. Terry, This just says that we estimate the velocity of a particle moving through a space by taking two points on its trajectory and dividing the distance traveled between them by the time it takes to do so. To get the instantaneous velocity at a point on the trajectory we take the limit of this quotient as pairs of points are chosen ever closer to the point of interest. We estimate acceleration by taking three points, taking the velocity between the first two, taking the velocity between the last two, then taking the rate of change in the velocities as an estimate of the acceleration. We get the instantaneous acceleration by choosing the three points ever closer and taking the limit. By the way ... This is probably a good time to mention an objection that is bound to arise in regard to Peirce's use of the series of quantities, Position, Velocity, Acceleration, to illustrate his 3 categories. There is nothing about that series, which can of course be extended indefinitely, to suggest that the categories of monadic, dyadic, and triadic relations are universal, necessary, and sufficient. Not so far as I can see, not right off, at least. So making that case for Peirce's Triple Threat will probably have to be mounted at a different level of abstraction. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey word press blog 1: http://jonawbrey.wordpress.com/ word press blog 2: http://inquiryintoinquiry.com/ --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to [email protected] with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to [email protected]
