Insert some data:
db.foo.insert({title:"A doc", intervals:[

{value:1, x:"a"}

,

{value:2,x:"b"}

,

{value:3,x:"c"}

]});

Verify it's there:
db.foo.find()
{ "_id" : ObjectId("4fd776800821eeb296a71a70"), "title" : "A doc", "intervals" : [

{"value" : 1, "x" : "a"}

,

{"value" : 2, "x" : "b"}

,

{"value" : 3, "x" : "c"}

] }

Try a projection:
db.foo.aggregate({$project:{title:1, i1:"$intervals.0"}})
{
"errmsg" : "exception: assertion src/mongo/db/pipeline/value.cpp:446",
"code" : 0,
"ok" : 0
}

Try another:
db.foo.aggregate({$project:{title:1, i1:"$intervals.0.value"}})
{
"errmsg" : "exception: assertion src/mongo/db/pipeline/value.cpp:446",
"code" : 0,
"ok" : 0
}