![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
![[identity profile]](https://www.dreamwidth.org/img/silk/identity/openid.png){kind=small}
A conversation tonight started me thinking about the natural distribution of units of length. Obviously some size ranges are of more importance to us than others. I could think of several groupings, but I had no idea how regularly the space would be filled. And while I can name quite a few units off the top of my head, being a metrology geek, there are certainly many more that I could use for comparison. So when I got home, I hit up Wikipedia and started building a spreadsheet.
This is by no means a comprehensive collection. I tried to get the all the major ones, which obviously implies a certain bias to those that have appeared in history I'm familiar with. I added a scattering of other ones that stood out when looking through Wikipedia, but there are vast realms of poorly understood historical systems not represented here. I didn't add minor variations, like the US surveyor's foot vs the Indian foot vs. the international foot. And I didn't add those based simply on the mechanical application of prefixes, but tried to restrict it to those which in my head actually get real use. So millimeter, centimeter, meter and kilometer are all represented, but not decimeter or megameter. Maybe someday I'll make a more rigorous version, but whatever. All units were represented as their equivalent in meters and plotted out in logarithmic form.
Tada! Source OpenOffice spreadsheet here, on Google Docs here. (That is, btw, one of my favorite graph titles I have ever penned.)
So, what does this tell us? First of all, lengths that interest humans are pretty symmetrically distributed (logarithmically speaking). Since my original question was "is it weird that I can't think of a unit between a ~mile and an AU?", I now have an answer: not really. The only inverse units which fill that space are the twip, the thou and the micron, and one of those is a pretty silly unit. (Also, I had forgotten about the league, and only learned about the mil tonight.)
Random observation: You can divide all the units into 5 rough categorizations as follows.
Most interestingly, I would argue that the distribution defines the optimal ur unit of length. It clusters pretty nicely around 0, that is, 100 AKA 1 AKA a meter. Which is nice for my SI imperialist instincts, but it's not exactly at 0. The median value is actually 0.2 which gives us 1.58 meters. This means the most basic, fundamental (to the human psyche) length is a toss up between the Roman pace and the smoot. Go figure.
Maybe I should go sleep now.
ETA: Whoops, I forgot nanometer, which I think would count. Oh well.
This is by no means a comprehensive collection. I tried to get the all the major ones, which obviously implies a certain bias to those that have appeared in history I'm familiar with. I added a scattering of other ones that stood out when looking through Wikipedia, but there are vast realms of poorly understood historical systems not represented here. I didn't add minor variations, like the US surveyor's foot vs the Indian foot vs. the international foot. And I didn't add those based simply on the mechanical application of prefixes, but tried to restrict it to those which in my head actually get real use. So millimeter, centimeter, meter and kilometer are all represented, but not decimeter or megameter. Maybe someday I'll make a more rigorous version, but whatever. All units were represented as their equivalent in meters and plotted out in logarithmic form.
Tada! Source OpenOffice spreadsheet here, on Google Docs here. (That is, btw, one of my favorite graph titles I have ever penned.)
So, what does this tell us? First of all, lengths that interest humans are pretty symmetrically distributed (logarithmically speaking). Since my original question was "is it weird that I can't think of a unit between a ~mile and an AU?", I now have an answer: not really. The only inverse units which fill that space are the twip, the thou and the micron, and one of those is a pretty silly unit. (Also, I had forgotten about the league, and only learned about the mil tonight.)
Random observation: You can divide all the units into 5 rough categorizations as follows.
- subatomic: fermi, angstrom
- precision fabrication: micron, thou, millimeter
- human: centimeter, inch, cubit, meter, fathom
- geometric (in the old sense): kilometer, mile, league, li, mil
- astronomical: AU, lightyear, parsec, spat
Most interestingly, I would argue that the distribution defines the optimal ur unit of length. It clusters pretty nicely around 0, that is, 100 AKA 1 AKA a meter. Which is nice for my SI imperialist instincts, but it's not exactly at 0. The median value is actually 0.2 which gives us 1.58 meters. This means the most basic, fundamental (to the human psyche) length is a toss up between the Roman pace and the smoot. Go figure.
Maybe I should go sleep now.
ETA: Whoops, I forgot nanometer, which I think would count. Oh well.
no subject