Re: C.S. Peirce • A Guess at the Rid dle

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

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