Arduino UNO - LCD and printing data from a webpage through serial

Hey people,

I picked up my arduino uno again after I was given a 40x2 LCD.
After playing around with it for a little I started thinking:

What if I hooked up the arduino to my laptop/netbook which is connected to the internet, and let's say I am listening to shortwave ham-radio through a websdr.
Wouldn't it be cool if the LCD was displaying the frequency the websdr is tuned into and maybe the modulation they are working in (AM/LSB/USB)

Would this even be possible?

I listen to this websdr all the time:
http://websdr.ewi.utwente.nl:8901/

I've seen projects in the past where stuff was displayed through a webpage, but they all used an ethernet shield for that which I don't have.

Would this even be possible?

Probably not. There is some interaction between the browser (a client) and the server. The client (the browser) can't talk to the serial port, so it has no way to get data to the Arduino.

If the Arduino was wearing an Ethernet shield, it could act like a client, too. But, it would not be the same client that the PC was, and there is no way for two clients to communicate.

Ah ok, that's too bad......
the idea was cool, but as I thought not possible.