![[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
I discuss something like this in my astronomy classes--when we do a scale drawing of the earth-moon system, and I point out the difficulties of the English system for that purpose (over on facebook, I've seen the most cogent argument for the English/US customary system--English units are cuddly and metric ones are spiky (probably because they have too many syllables).
Anyway, looking at the origin of the meter, it simply the distance that was an integral negative power of ten times a quarter of the earth's circumference that seemed most human-friendly. From this persepective, as a model maker, and craftsman of the small, I found the meter to be ten times bigger than I would choose.
Your finding of 1.58 meters for the median unit is interesting to me, as that falls within the range of median heights of humans for various countries given at this website (http://www.shortsupport.org/Research/international.html) (the first google hit with broad data that I stumbled into). The median unit is on the short side--below the median for men in all the countries listed, and shorter than women in 9/12 of the countries listed.
If those statistics were weighted for population, I think the median unit would still be short for the median human, but perhaps close to the height of a median woman.
Hmm...I wonder if you could find a moment in history when the median height of an adult human was 1.58 meters--about 5' 2" in dog years.
I think it's not surprising that humans measure the world against themselves.