St. Augustine has a problem: what is time and how do we measure intervals of time? St.
Augustine argued that time cannot be due to the movement of the heavenly bodies, because even
the sun stopped when Joshua commanded it to do so:
Therefore, I will not now ask what is it that is called a day, but rather what is time, by
which we would measure the sun's circuit and say that it was completed in half the time it
usually takes, if it were finished in a period of twelve hours. Comparing both times, we
should call the one a single period, the other a double period, even if the sun ran its course
from east to east sometimes in the single period and sometimes in the double.
Let no man tell me, then, that movements of the heavenly bodies constitute periods of time.
When at the prayer of a certain man, the sun stood still until he could achieve victory in
battle, the sun indeed stood still, but time went on. That battle was waged and brought to an
end during its own tract of time, which was sufficient for it. Therefore, I see that time is a
kind of distention. Yet do I see this, or do I only seem to myself to see it? You, O Light,
will show this to me. (Confessions of St. Augustine, Book 11, Time and Eternity, p. 296)
St. Augustine described time here as a kind of distention, an expansion beyond its normal
length in the same way as when we say that a bowel or lungs become distended. The modern
concept for this time dilation in Special Relativity. But from the first paragraph that we
quoted, we can see that St. Augustine is clear on what he means by time: a fixed scale that
allows us to compare short days of summer with the long days of winter. In this sense, what
St. Augustine really wants to say is that time is a scalar quantity.
Scalar quantities are quantities that can be described by a scale of measurementquantities
such as "depth and breadth and height" in Elizabeth Browning's poem, "How do I love thee?"
These quantities can be described by the same unit of measurement for length: the meter. Note
that poems have their own definition for meters which Augustine also mentioned to compare long
and short syllables:
Deus creator omnium"God, creator of all things"this verse of eight syllables alternates
between short and long syllables. Hence, the four short syllables, the first, third, fifth,
and seventh, are simple with respect to the four long syllables, the second, fourth, sixth, and
eighth. Each long syllable has a double time with respect to each of the others. This I
affirm, this I report, and so it is, in so far as it is plain to sense perception. (Confessions of St. Augustine, Book 11, Time and Eternity, p. 296)
But aside from length, there are other scalar quantities in physics: pressure (measured in
millimeters of height of the Mercury column), resistance (as seen from the multimeter scale),
and, of course, time (as seen from an analog watch with scales marked in equal intervals in a circle).
Scales need not be uniform. One example is the logarithmic scale which we used in slide
rulesthe computers in bygone age when electronic calculators and computers were not yet
invented. The equal intervals in the slide rule scale are based on the powers of 10, which
allows the multiplication, division, and raising to the power of large numbers possible in
terms of addition, subtraction, and simple multiplication. For example, a timeline that uses
the logarithmic scale is the Big Bang Theory.
Aside from the logarithmic scale, you can actually invent many kinds of scales, but the
important thing is that the scale must have a function or an equation that maps the real
numbers in a number line to your chosen scale. For example, if you use a linear scale, the
function may simply be $y=mx$, where x is a real number, $y$ is your scale, and $m$ is a
constant parameter. But if you use a logarithmic scale, then $y=10^x$. 
