What distance is twice as close as 10 metres?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

16 May 2021

On May 11, popular astrophysicist, Dr. Neil deGrasse Tyson posted this message on Twitter: “Not to worry, the Moon’s been spiralling away from us for nearly 4.5 billion years, shortly after the Solar System was born. Back then, the Moon was in-your-face: It orbited Earth every 8 hours, was 20x closer, 400x larger on the sky, and forced tides 8,000x stronger than today.”

When I read it, my mind went back to the year 2007 when a reader asked me what temperature is twice as cold as zero degrees. Since zero multiplied by anything is still zero, one might be tempted to conclude that twice as cold as zero degrees is zero.

However, before answering the question, one must clarify which temperature scare is being used. Is it celcius or fahrenheit or kelvin or what? Furthermore, how is coldness measured?

A similar question may be same can be asked of Dr. Tyson’s statement: how is closeness measured? The only way I can think of it is as the inverse of distance. Thus, if something is, say, 10m away, it can also be said to be 0.1/m close (read as “0.1 per metre”); that is, the inverse of 10, or, 1 divided by 10.

Now, if this object is moved to a position that is twice as close as the original, then it would come from a closeness of 0.1/m to 0.2/m. So, how far away is that?

Since we have defined closeness as the inverse of distance, it follows that distance is also the inverse of closeness. Therefore, a closeness of 0.2/m is equal to a distance of 1 divided by 0.2; that is, 5m.

So, the statement that something is twice as close simply means that it is half the distance. Consequently, by saying that the moon used to be 20 times closer, what Dr. Tyson meant was that it was a twentieth of the present distance.

It may seem confusing but this is not the only situation where we use the inverse of a quantity. The most common is the fuel consumption of motor vehicles. It is usually stated in kilometres per litre (km/L).

So, if car-X does 10km/L and car-Y 15km/L, which of the two consumes more fuel? The answer is X, of course! But why do we all agree that 10km/L is a higher consumption rate than 15km/L, yet the number 10 is lower than 15?