2
votes
0answers
130 views

Information content of universal sentence

What is the information content of a sentence S like 'one has a successor'. To me, it looks like if we assume no a priori knowledge, both S and it's negation will have equal probablity 1/2. This is ...
11
votes
3answers
271 views

What is necessary to exchange messages between aliens? [closed]

Lets assume that two extreme intelligent species in the universe can exchange morse code messages for the first time. A can send messages to B and B to A, both have unlimited time, but they can not ...
7
votes
3answers
195 views

Measure of how much information is lost in an implication

In an implication like $p \implies q$, is there some measure of how much information is lost in the implication? For example, consider the following implications, where $x \in \{0,1,\ldots,9\}$: ...
2
votes
2answers
100 views

Numbers which encode other numbers infinite times.

Let $g(x,n)$ be a function which chops off the first n digits of the binary decimal expansion of x. eg $g(0.1010111,2)=0.10111$ Is there a function $f(x)$ from the reals to the reals, such that for ...