mathematical time – Will Johncock

Samuel Blankson describes cultural time as a human, quantifiable invention. The time that is being quantified, natural time, would not manifest in measurable ways, if not for human intervention.

…relation between points brings into question the origin of points. Since that is human, it still means man is part of the definition of time, an uncomfortable notion for all those mathematicians who believe that time occurs as a natural entity without human intervention so that it can be treated materially with mathematics alone.

Let me explain that I agree (or I know) that there is such a thing as natural time, of course. But cultural time, as quantified time (that is ‘something’ quantified or extracted from natural time), is a human invention – somebody must be there to count the orbits of the sun as ‘years’ or there will be no years and no seconds derived as fractions of the year (Blankson 2011, 14-15).

Blankson, Samuel K.K. (2011). The logic of time in the universe: A critique of Professor Yourgrau’s “World without time”. Morrisville: Lulu.

Pitrim Sorokin and Robert Merton differentiate between a purely quantitative constitution of astronomical, mathematical time, and qualitatively differentiated constitutions of social times. Social times are said to use what is homogeneously regular about astronomical time for the development of calendars and rituals.

The system of [social] time varies with the social structure. Astronomical time is uniform, homogeneous; it is purely quantitative, shorn of qualitative variations. Can we so characterize social time? Obviously not-there are holidays, days devoted to the observance of particular civil functions, “lucky” and “unlucky” days, market days, etc. Periods of time acquire specific qualities by virtue of association with the activities peculiar to them. We find this equally true of primitive and more complex societies…

Summing up, we may say that thus far our investigation has disclosed the facts that social time, in contrast to the time of astronomy, is qualitative and not purely quantitative; that these qualities derive from the beliefs and customs common to the group and that they serve further to reveal the rhythms, pulsations, and beats of the societies in which they are found.

Mathematical time is “empty.” It has no marks, no lacunae, to serve as points of origin or end. Yet the calendar-maker requires some sort of starting-point or fixed datum. Some beginning, arbitrary or not, must be set in order to initiate any system of time reckoning which purports to be continuous (Sorokin and Merton 1937, 621-23).

Sorokin, Pitrim, and Merton, Robert. 1937. ‘Social time: A methodological and functional analysis.’ The American journal of sociology 42(5): 615-29.