"Wrong, they are exactly the same distances. I r..."


by Eyal Roth Mar 18 2019 updated Mar 18 2019

Evidence you are twice as likely to see if the hypothesis is true than if it is false is $~${+1}$~$ bits of evidence and a $~${^+1}$~$\-bit update, regardless of how confident or unconfident you were to start with\-\-the strength of new evidence, and the distance we update, shouldn't depend on our prior belief\. If your credence in something is 0 bits\-\-neither positive or negative belief\-\-then you think the odds are 1:1\. The distance between $~$0.01$~$ and $~$0.000001$~$ is much greater than the distance between $~$0.11$~$ and $~$0.100001.$~$

Wrong, they are exactly the same distances. I read the next paragraph so I get where you were going with this, but I find it confusing to start off with a blatantly wrong claim, especially when the next line compares 0.11 to 0.1 (11% to 10%) -- not to 0.100001 -- in order to describe how the significance of 0.00001 gets "lost in translation" when speaking in probabilities and not in bits.