[TriLUG] IPv4 routing I don't understand...

[Brian Henning via TriLUG]

Hi Folks,

I was hoping someone could help me understand a weird behavior I'm seeing when my home network routes to the outside world.  Here's the scenario:

 [gateway router    ] 
[eth1:192.168.0.80/24]
[eth0:71.70.212.129/22] 
     |
 [ bridge modem ]
     |
 { the great beyond }

The external interface is cabled to the modem which is [supposed to be, presumed to be] in bridging mode.

Here is the gateway's routing table:
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
192.168.0.0     0.0.0.0         255.255.255.0   U     0      0        0 eth1
10.32.4.0       0.0.0.0         255.255.255.0   U     0      0        0 eth1
10.1.1.0        0.0.0.0         255.255.255.0   U     0      0        0 vmnet8
71.70.208.0     0.0.0.0         255.255.240.0   U     0      0        0 eth0
169.254.0.0     0.0.0.0         255.255.0.0     U     0      0        0 eth1
0.0.0.0         71.70.208.1     0.0.0.0         UG    0      0        0 eth0

Here is a traceroute to a well-known DNS server (with timing omitted for space):
traceroute to 8.8.4.4 (8.8.4.4), 30 hops max, 40 byte packets
 1 192.168.0.1  
 2 71.70.208.1  
 3 66.26.47.197  
 4  24.25.62.178  
 5  24.93.64.186  
 6  107.14.19.48  
 7  107.14.19.11  
 8  216.156.108.97  
 9  216.156.108.114  
10  209.85.240.243  
11  64.233.175.225  
12  8.8.4.4  

Why is 192.168.0.1 in there?  There is no device at 192.168.0.1 on my network, and no reason for it to hop there first seems evident in the routing table.

I've known TWC modems to "forget" they're bridged; could that be the cause?  eth0 is addressed via DHCP, and refreshing its lease gives it the same publicly-routable address.

Thanks,
-B