Yesterday at work I downloaded a 96MB file from a vendor web site in Texas to my workstation on the 19^th floor of our building. It took about 5 minutes. Today I tried to copy it from my workstation to a server in the Data Center, in the basement. The first time I tried a windows copy. It timed out after about 20 minutes. My second try used FTP, which allowed me to monitor the progress. I killed the process after about two hours, after calculating that it would not finish until over 42 hours had elapsed. I then logged on to the server, connected to the vendor site again from there, and downloaded the file directly to the server. It took about 5 minutes this time as well.

So, we have 3 points:

• A – My desk
• B – The vendor site
• C – The Data Center.

With distances

• AB = about 1000 miles
• BC = about 1000 miles
• AC = 20 stories, or somewhere around 300 feet

I enjoy looking at strange maps, where geography is distorted by some other measure, e.g. this. So I tried to imagine a map of my three point using network time as a measure of distance. We have:

• AB = 5 minutes
• BC = 5 minutes
• AC = 42 hours

It cannot be done in any normal geometry (try drawing a picture). The network times fail the Triangle Inequality, which requires that

AC ≤ AB + BC

Of course, I was measuring AB and BC by download times. Upload times might be different, though I doubt they would come close to 42 hours.

Also, the Wikipedia article reminded me that in Minkowski space the Triangle Inequality is reversed:

AC ≥ AB + BC

Minkowski space (actually Minkowski space-time) is used in special relativity, where it resolves the “twin paradox”.

So, my network times would makes sense if this part of the network were in a Minkowski space!