Thought for the Day

I've been thinking about 4-dimensional volume recently, mostly: What units would we use? My best guess is m⁴, like Volume is m³ and Area is m².

But I can't keep referring to it as 4-d volume, so I'll call it Occupation (on the basis that the four dimensions are length, depth, height, and duration), with a symbol of j (those truly keen will understand why). So:

j = l * d * h * t

But duration is measured in seconds, normally, so the equation above would get me units of m³-s (meter cubed-seconds). I certainly can't leave it like that! If I wanted to know the surface area of a table that was 20 inches long and .5 meters wide, I certainly wouldn't say that the area was 10 meter-inches. I would convert either the 20 in to meters, or the .5 m to inches. So I should change the units of j so that it is simply m⁴, and that leads to this question:

How many meters are in a second?

If the answer to this question was known, then one could find the Occupation of an object, when one knows its volume and duration.

Some people might say that the velocity of the object answers the question. But velocity is variable; the answer to the question should be a constant, like how many meters are in a mile (approx. 1619 meters in a mile).

Until next time, remember: Think on tangents--you'll go farther than those who stay with the curve.

---TDM