It takes more than twice as many bits to describe two sheep than it takes to describe a single sheep, because, in addition to those two sheep, you now also have to describe their relationship to one another.
On the other hand you don’t have to describe twice features shared by both sheep.
I would argue that this is a form of “encoding” and “compressing” of the data, and that in a strictly atomic sense would produce a fuzzy description unless both sheep actually shared their atomic components. I use the word “atomic” here to refer to whatever form of most elementary description tickles your fancy, be it strings or wave functions or quarks or bosons or gluons or what-have-yous—the most elemental and fundamental pieces with which the two sheep are built, whatever that may truly be.
Arguably, and I’m really not sure about this second hypothesis, the Total Message Length might turn out to be even greater than before if you attempt to produce any sort of “accurate” description of both sheep by way of “shared features”.
On the other hand you don’t have to describe twice features shared by both sheep.
I would argue that this is a form of “encoding” and “compressing” of the data, and that in a strictly atomic sense would produce a fuzzy description unless both sheep actually shared their atomic components. I use the word “atomic” here to refer to whatever form of most elementary description tickles your fancy, be it strings or wave functions or quarks or bosons or gluons or what-have-yous—the most elemental and fundamental pieces with which the two sheep are built, whatever that may truly be.
Arguably, and I’m really not sure about this second hypothesis, the Total Message Length might turn out to be even greater than before if you attempt to produce any sort of “accurate” description of both sheep by way of “shared features”.
Very true. One alien intelligence might count 1.3, instead of 2, or 2.08.