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

https://arbital.com/p/9h9

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.