The Glass is Mostly Half Empty

Sometimes I get asked what type of a person I am, “a glass half empty” or “glass half full”. This question is really not about how much liquid I think there is in a cup, it's more about your attitude. Are you the type that sees the world as a happy and functional place or are you the type that sees the world in a state of imperfection that needs to be repaired. This is a hard question to answer as it seems that the amount of water in a glass changes frequently.

My dad is somewhat a glass half empty kind of guy. My mom and sister are definitely a glass half full.  I am somewhere in the middle.  To find out once and for all, I decided to spend some of the time and figure it out.

I thought that the easiest way to settle the question would be to actually check the amount of water in a glass.  We drink a lot of water in our house and have plenty of glasses. After examining our cupboard, I have found that they come in one of the following 3 shapes:

1. Glasses with the walls tapering upwards 
2. Glasses with the walls tapering downwards
3. Glasses with parallel walls

Beyond the differences in glass geometry (its shape and size), I also noticed that the base of many glasses has a thick solid section that keeps them from easily tipping over (my dad says that it has to do with increasing the glasses overall Moment of Inertia-which I don’t really understand yet).   Another interesting thing about the interior bottom section of the glass is that its outline is almost always curved (which makes volume calculations difficult).

The Experiment My “glass half full\half empty” experiment was simple and you can repeat it yourself in just a few minutes without any special equipment.  I used 2 drinking glasses, a small container, a ruler, a  marker, and a pitcher of water. To make sure that my experiment was valid, I used 2 different types of glasses, each with opposite geometry (glass A  tapered downward and glass B tapered upwards).  Here’s what I did:

1. For each glass, I found the halfway line by measuring its
     overall height and dividing it in half. 
2. I marked the halfway point with a black line. 
3. I filled glass A with water up to the halfway line.

 
Glass A (halfway line)   Glass B (halfway line)

4. I then emptied the water from glass A into a beaker
5. I refilled glass A up to to the halfway line again.
6. I added the water from the beaker back to glass A.
7. I repeated the same steps for glass B

After refilling both glasses, It became apparent that regardless of the glass geometry or the thickness of the base, the halfway mark contained less than half of the amount of water the glass could hold.

 
         Glass A (Full)                     Glass B (Full)
So next time someone asks you if you are a glass half full or a glass half empty type of a person, you can tell them with confidence that you just happen to know for a fact that all glasses are just a little more than half empty.