Of course, zip code and birthday are a pretty huge amount of information. With the simplifying assumptions of roughly uniform distributions, knowing a birthday confers ~8.5 bits and knowing your zip code is worth ~15 bits. That's 23.8 in total.

It's not surprising that those two pieces of information can pretty easily narrow down an identity.

  log2(3*10^8) = 28.2

Birthday encodes a lot more than one bit of information. The above example was a series of factors that reduced the identified population in half.

Alright; would you prefer me to redo it with pieces of information each worth 7 bits?

'The first piece cuts it down to 2.3 million people...'