There is an app called WiFi File Explorer that lets the eDGe serve up its directory as a web page to other machines on your network. I picked up the PRO version on a Free App Of The Day, so I'm not sure about the differences between it and the free (non-pro) version.
(linky clicky appstore goodness)
AH. More info from the app's page:
"Once your phone is connected to the Wi-Fi network, it's easy to go to the computer (which must also be connected to the network) and access the Web address. You'll find that your phone's files are there to be browsed, downloaded, or even streamed whenever you wish.
In this PRO version, you can also upload, sync, delete, copy, and zip or unzip all the files on your Android phone and computer, which makes it a great overall file manager.
A free version of this app, simply called WiFi File Explorer, is available as well. It offers similar but less robust features."