Tuesday, January 26, 2010

The Glass is Mostly Half Empty

The Glass is half empty-Sheva Apelbaum 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, its 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 glass half full.  I am somewhere in the middle.  To find out once and for all, I decided to spend some the time and figuring 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.

Tapered down glass half full-Sheva Apelbaum Taperd up glass half full - Sheva Apelbaum
      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. 

Tapered down glass full-Sheva Apelbaum Tapered up glass full-Sheva Apelbaum
               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.


  1. Wow--that is something I've always asked myself! And actually, taking into account that there is a certain amount of evaporation, I would say I am a glass half full till that evaporation becomes noticable, and then I am more than half empty...good thing there is a faucet (books, ideas, movies) in our house! Thank you again, Sheva, for a most wonderful post!

  2. :|
    >(^.^)> <(^.^)<


  3. Dawn: I never thought about the evaporation process that happens. I guess that even if you are glass half full, evaporation will eventually make you a glass half empty!

    Yael: Thank you for the wonderful message!♥
    (>'3')>-----------<3 back to you. You are such an O:-)
    You can only imagine the big :-D on my face !

  4. Sheva and Dawn, this is a VERY interesting thought:
    ...even if you are glass half full, evaporation will eventually make you a glass half empty...
    Since we are speaking metaphorically, evaporation could be any given life experience!
    But I also think like Dawn, that the glass could be balanced at the half full line - every one could choose his favorite fillers - mine and my husband would be definitely enjoying nature in all it's splendors (among other things of course, friends being a big part of it).