Is there any sort of advantage (performance, indexes, size, etc) to storing dates in MongoDB as an ISODate() vs. storing as a regular UNIX timestamp?
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The amount of overhead of a ISODate compared to a time_t is trivial compared to the advantages of the former.
An ISO 8601 format date is human readable, it can be used to express dates prior to January 1, 1970, and most importantly, it isn't prey to the Y2038 problem.
This last bit can't be stressed enough. In 1960, it seemed ludicrous that wasting an octet or two on a century number could yield any benefit as the turn of the century was impossibly far off. We know how wrong that turned out to be. The year 2038 will be here sooner than you expect, and time_t are already insufficient for representing – for example – the schedule of payments on a 30-year contract.
MongoDB's built-in Date type is very similar to a unix timestamp stored in time_t. The only difference is that Dates are a 64bit field storing miliseconds since Jan 1 1970, rather than a 32bit fields storing seconds since the same epoch. The only down side is that for current releases it treats the count as unsigned so it can't handle dates before 1970 correctly. This will be fixed in MongoDB 2.0 scheduled for release in about a month.
A possible point of confusion is the name "ISODate". It is just a helper function in the shell to wrap around javascript's horrible Date constructor. If you call either "ISODate()" or "new Date()" you will get back the exact same Date object, we just changed how it prints. You are still free to use normal ISO Date stings or time_t ints without using our constructors, but you won't get nice Date objects back in your language of choice.