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.

7 thoughts on “Fundamental units”

1. John Thacker

The most ridiculous example was with the “1.44 MB” floppy disk. This was 1440 (binary) kilobytes, defining “megabyte” to be “1000 x 1024 bytes,” an extremely odd choice of unit that nevertheless usually didn’t matter in informal practice. (Having to refer to 2^10 * 10^3 is strange, though.)

2. That was strange. I never thought about it, but I would have assumed by “MB” they meant either 10^6 or 2^20, not some unholy hybrid of the two. :)

3. In Quantum Chemistry and Physics our fundamental units are not SI, they’re “atomic units” where the charge of an electron is 1, the mass of an an electron is 1, and hbar is 1. It makes computation really easy when everything is 1.

4. I now have two new imaginary friends for my undergraduate lecture examples: Kibi and Mibi! Thanks.

5. And if you need more, there’s tebi, pebi, exbi, zebi, and yobi. :)

6. Matthew Healy

The OTHER big difficulty with doing physics calculations in English units is less obvious: the fact that it was defined before people understood the difference between mass and weight. Thus we have both a pound as a unit of mass and a pound as a unit of force. Which means we have to multiply or divide by 32.17405 ft/s2 in lots of less-than-intuitive places. I find it easier to convert to SI than keep straight when to multiply or divide by g!

7. Steve Alexander

Interesting that you could tell the same kind of story about the Byte.

https://en.wikipedia.org/wiki/Byte

8 bits? Perhaps, depends when and where you’re asking.

byte bit as second Planck time, in some sense.