ている is not 'is doing'. It is a switch left on.

Where the picture shows up in ている

1. 1

   still running

   今、昼ご飯を食べています。

   ima, hirugohan o tabete imasu

   I'm having lunch right now.

2. 2

   left on for good

   母は大阪に住んでいます。

   haha wa ōsaka ni sunde imasu

   My mother lives in Osaka.

   Plain 住みます sounds wrong. Living somewhere is a switch that stays on, so 住んでいます is the normal form.

3. 3

   the result is still on

   電気がついています。

   denki ga tsuite imasu

   The light is on.

4. 4

   a habit kept switched on

   毎朝、六時に起きています。

   maiasa, rokuji ni okite imasu

   I get up at six every morning.

5. 5

   it became so and stayed

   姉は結婚しています。

   ane wa kekkon shite imasu

   My sister is married.

   結婚しました is the wedding as an event; 結婚しています is being married now.