Updated FAQ (markdown)

FAQ.md

@@ -1,3 +1,58 @@
-# Frequently Asked Questions
+##Contents
+- [Why can't I do day arithmetic on a `year_month_day`?](#day_arithmetic)
 
-Why can't I do day arithmetic on a `year_month_day`?
+***
+
+<a name="day_arithmetic"></a>
+### Why can't I do day arithmetic on a `year_month_day`?
+
+This library is meant to be a foundational library upon which you can efficiently build higher-level date libraries (like tz.h). A core component of this library is that it makes expensive computations explicit, so that you can see where they are in your code. Higher-level code can hide these expensive/explicit operations as desired.
+
+A good way to estimate the cost of any given date computation is to count the number of conversions from a field type (e.g. `year_month_day` or `year_month_weekday`) to a serial type (e.g. `day_point`), and vice-versa.  As an example, here is a real-world example (found in the issues list):
+
+We need to compute the day after the 3rd Tuesday of the month.  If day-oriented arithmetic was allowed on `year_month_weekday`, that would be in the form of a function like this:
+
+    constexpr
+    year_month_weekday
+    operator+(const year_month_weekday& ymwd, const days& dd) noexcept
+    {
+        return year_month_weekday{day_point{ymwd} + dd};
+    }
+
+The programmer would probably use it like this:
+
+    year_month_day
+    get_meeting_date(year y, month m)
+    {
+        return year_month_day{tue[3]/m/y + days{1}};
+    }
+
+That is super-compact syntax!  Here is what it costs:
+
+1. Convert `tue[3]/m/y` (`year_month_weekday`) to `day_point` in order to add `days`.
+2. Convert the `day_point` computed back to `year_month_weekday`.
+3. Convert the temporary `year_month_weekday` computed in 2 back to `day_point`.
+4. Convert the `day_point` to a `year_month_day`.
+
+4 conversions.
+
+Here is the way you have to write this function today (because `tue[3]/m/y + days{1}` is a compile-time error):
+
+    year_month_day
+    get_meeting_date(year y, month m)
+    {
+        return year_month_day{day_point{tue[3]/m/y} + days{1}};
+    }
+
+The syntax is slightly more verbose in that you have to explicitly convert the `year_month_weekday` into a `day_point` in order to perform the day-oriented arithmetic.  Here is what it costs:
+
+1. Convert `tue[3]/m/y` (`year_month_weekday`) to `day_point` in order to add `days`.
+2. Convert the `day_point` to a `year_month_day`.
+
+2 conversions.  Roughly twice as fast!
+
+This philosophy is similar to that which we have for containers:  It would be super easy to create `vector<T>::push_front(const T&)`.  But that would make it too easy for programmers to write inefficient code.  The compiler helps remind the programmer that perhaps `deque<T>` or `list<T>` would be a better choice when he attempts to code with `vector<T>::push_front(const T&)`.
+
+It would be very easy to add `T& list<T>::operator[](size_t index)`.  But that would encourage the programmer to use `list<T>` when a random-access container would probably be more appropriate for the task.
+
+This library continues in that tradition:  The expensive operations are not hidden.