Fundamental units

It’s much easier to convert meters to kilometers than to convert yards to miles. You know what’s even easier? Not converting meters to kilometers!

You only need one unit of length, say a meter. You could express all distances in terms of meters and dispense with kilometers, millimeters, etc. And in fact, this is essentially what science does. It hardly makes a difference whether you say the Andromeda galaxy is 2.365 × 10²² meters away or 2.365 × 10¹⁹ kilometers away. Especially if you need scientific notation anyway, you might as well use base units.

Multiple units for the same fundamental quantity are psychologically convenient though not logically necessary. Astronomers, for example, simply use meters for calculation. But they may use other units such as AUs or light years for conceptualization and communication. Scientists do all time calculations in seconds, though it’s easier to understand long time scales in units of years.

It’s commonly said that it’s easier to do science in SI units than in imperial units. This is in some sense true, but it would be more accurate to say it’s easier to do science in terms of fundamental units. The SI prefixes kilo, mega, etc. are a sort of intermediate step to letting go of all but fundamental units.

One could imagine an alternative history in which science standardized on the inch rather than the meter. Distances like yards and miles could have been seen as auxiliary units for conceptual purposes, much like the astronomical unit and light year.

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This post was motivated by an online discussion of kilobytes and megabytes. I said something about a kilobyte being 1,000 bytes, and someone replied saying technically this should be 1,024. I replied saying that even more technically, it’s 1,000 bytes. This is a good example of coming full circle. The least informed and most informed agree, while those in the middle disagree.

You might naively assume that because 1,000 grams is a kilogram that 1,000 bytes is a kilobyte. But for years, a kilobyte was commonly understood to mean 1,024 bytes. To address the confusion, the IEC introduced new prefixes such as kibi and mebi in 1998. Now a kibibyte is 2¹⁰ = 1,024 bytes, a mebibyte is 2²⁰ = 1,048,576 bytes, etc. And so a kilobyte now refers to 1,000 bytes, just as one might naively have assumed.

In practice the difference hardly matters. If you want to indicate exactly 2²⁰ bytes, you can say “one mebibyte.” But in my opinion it’s even better to simply say “2²⁰ bytes” because then there is no chance of being misunderstood.

To my mind, terms like “megabyte” are something like light years, i.e. conceptual units. Whether you think a megabyte is exactly a million bytes or approximately a million bytes doesn’t matter in informal communication. If it’s necessary to be precise, simply state the number of bytes as an integer, using powers of 10 or 2 if that helps.

The purpose of communication is to be understood, not to be correct. If you use megabyte to mean exactly 1,000,000 bytes, you may be correct according to the IEC, but you run a significant risk of being misunderstood. Better, in my opinion, to just use the fundamental unit bytes.

I made a similar point in my post on names for extremely large numbers. When you use these names, there’s a good chance your listener will either not know what you’re talking about, or worse, misunderstand what you mean.