At the Senate Judiciary Committee’s subcommittee on privacy, technology and law Tuesday, Sen. Al Franken put his finger on the most glaring contradiction in the controversy that has come to be known as Locationgate:

On the one hand we have Steve Jobs telling All Things Digital‘s Ina Fried that the location data Apple (AAPL) gathers from iPhone users “are not telling you anything about your location.”

On the other, we have Apple’s Q&A, issued the same week, claiming that data stored on each iPhone will “help your iPhone rapidly and accurately calculate its location.”

“It does not appear to me,” Franken told Guy L. (“Bud”) Tribble, who was representing Apple at the hearings, “that both these statements could be true at the same time.”

It turns out, as Tribble took pains to explain, that Franken was conflating two databases, a huge, crowd-sourced one that Apple maintains, and the much smaller subsets downloaded onto each iPhone as they are needed.

Of course, Tribble’s answer and Steve Jobs’ assurances would be of no comfort to the unfaithful husband whose wife discovered — by mapping his iPhone data — that he did not spend the weekend in the country with his golfing buddies, but in the city, presumably with his mistress.

Franken, however, did not have the wit to ask the follow-up.

Below: The transcript of their exchange. (For the record, “data” is a plural noun, but we’ll spare you the [sic]s.)

Frankin: Mr. Tribble, last month I asked Apple in a letter why it was building a comprehensive location database on iPhones and iPads and storing it on peoples’ computers — when they synced up, of course. Apple’s reply to my letter will be added to the record. But this is what Apple CEO Steve Jobs said to the press: “We build a crowd-sourced database of Wi-Fi and cell tower hot spots but those can be over 100 miles away from where you are. Those are not telling you anything about your location.”

Yet in a written statement issued that same week, Apple explained that this very same data will “help your iPhone rapidly and accurately calculate its location.” Or as the Associated Press summarized it “the data help the phone figure out its location, Apple said.”

But Steve Jobs that same week said “those are not telling you anything about your location.”

Mr. Tribble, it does not appear to me that both these statements could be true at the same time. Does this data indicate anything about your location or doesn’t it?

Tribble: Senator, the data that’s stored in the database is the location of as many Wi-Fi hotspots and cellphone towers as we can have. That data does not actually contain — in our databases — any customer information at all. It’s completely anonymous. It’s only about the cellphone towers and the Wi-Fi hotspots. However, when a portion of that database is downloaded onto your phone, you phone also knows which hotspots and cellphone towers it can receive right now. So the combination of the database of “where are those towers and hotspots” plus your phone knowing which ones it can receive right now is how the phone figures out where it is without the GPS.

Get it?

Click here for a link to the webcast.