# Bias and the Liar [closed]

A cylindrical glass has water half its height

Some say it's half full, while some say it's half empty

But if Clair the liar mostly tell what's not right

Will she say "it is full" or she'll say "it is empty"?

• I think cylindrical might be a red herring. Man I love when there is a story. Commented Oct 6, 2016 at 20:25
• not a tapered glass
– TSLF
Commented Oct 6, 2016 at 20:34

She will say

It is empty

Because

Say we have a glass height $10cm$. The glass has to have a bottom, otherwise the water would fall out. Let's say the bottom is $1cm$.

The water is $5cm$ high when placed in the glass. Add the $1cm$ and you get $6cm$. This makes it more full than empty thus as she lies, it is empty

• Is this supposed to be lateral-thinking? Commented Oct 6, 2016 at 20:27
• Yes, sort of @Matsmath Commented Oct 6, 2016 at 20:28
• Assume it is as unlikely to make 1g of water appear from nothing as it is unlikely to make 1g of water disappear to nothing. She ought to choose between false and falser.
– TSLF
Commented Oct 6, 2016 at 20:44
• full is 100% height
– TSLF
Commented Oct 6, 2016 at 20:54

She will say that the glass is in a quantum entanglement state being both full and empty at the same time. Or more precisely:

$$\frac{|full\rangle + |empty \rangle}{\sqrt{2}}$$

This state persists until a measurement of the glass state is done. At that time, the glass wave-function will collapse into one of the states $| full \rangle$ or $| empty \rangle$, each one with $50 \%$ of probability of becoming reality.

I think she would say

It is empty, because it obviously contains a reasonable amount of water. It also obviously isn't "Full" but, one might say a glass is full at 75-80% of its theoretical maximum capacity if it might need to be lifted or transported, whereas one wouldn't say that a glass with as little as 10% of it's maximum capacity is empty. This means that the glass is closer to full than to empty, and so our Liar will say "Empty"