adding and incrementing date and time (Postgresql)

Your data model is pretty borked. You're storing at least two pieces of redundant information. You need starts and file_id and any one of clip_length, ends or position; they can each be calculated from each other.

Right now you are storing redundant data, which creates the problem you now have where the data is not internally consistent, it has conflicts within its self.

In this case it sounds like position is trusted and the others aren't. Here's what I'd do:

SELECT 
  (SELECT min(starts) FROM Sometable)
    + COALESCE(
       sum(clip_length) OVER all_rows_but_last,
       INTERVAL '0' second
    )
  AS starts,
  (SELECT min(starts) FROM Sometable)
    + COALESCE(
       sum(clip_length) OVER all_rows_but_last,
       INTERVAL '0' second
    ) + clip_length
  AS ends, 
  position, 
  clip_length
FROM Sometable
WINDOW all_rows_but_last AS (ORDER BY position ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING);

see: http://sqlfiddle.com/#!12/ca5fa/1

The principle here is to find the lowest start - the one known to be valid - and ignore the following ends and starts as redundant and useless. Instead, add the running total of the previous durations as the start, and the same running total plus the current interval as the end.

You'll notice that this isn't an update. That's because I think you should actually:

• change position to a floating point value or large integer so you don't need to re-number when you insert an entry. If you put something between 1 and 2 give it position 0.5. Or start with 10000, 20000 etc so you can insert 15000.

• Get rid of the ends column completely. calculate it from starts + clip_length

• Move starts to a separate table where it's stored only once, for the series of segments. Calculate clip start times on the fly from the sum of the lengths of previous clips since the start.

• Re-define the current table as a view over the two tables described above.

That's making a lot of guesses about your data and how you're using it, but you haven't said much about what you're doing.

with cte as (
    select
        '2013-08-30 22:00:00'::timestamp
         + sum(clip_length) over(order by position) as ends,
         file_id
    from clip
)
update clip as cl set
    starts = c.ends - cl.clip_length,
    ends = c.ends
from cte as c
where cl.file_id = c.file_id;

=>sql fiddle

Actually, you could live without start and end time in your table at all. You can remove this columns from your table and create function like this:

create or replace function clip_layout(_starts timestamp)
returns table(
    starts timestamp, ends timestamp,
    "position" int, file_id int,clip_length interval
)
as
$$
with cte as (
    select
        _starts + sum(clip_length) over(order by position) as ends,
        file_id, clip_length, position
    from clip
)
select
    ends - clip_length as starts,
    ends, position,
    file_id, clip_length
from cte
$$
language sql;

So you can see start/end times starting from anytime:

select * from clip_layout('2013-08-30 22:00:00'::timestamp)

=>sql fiddle demo