- Edited
Jose Luis Perez Velazquez
P.P.S.
"I prefer A. T. Winfree's perspective, as he said in his book 'The Geometry of Biological Time': "My deeper motivation is a feeling that numerical exactitude is alien to the diversity of organic evolution, and pretense of exactitude often obscures the qualitative essentials that I find more meaningful"
Here is my analysis of the situation: Looking at the work that physicists do, it is clear that the only types of information that they deal with are categories, relationships between these categories, and numbers that apply to these categories. The categories are measurable, and the result of measurement is a number, but the crucial relationships (represented via the use of mathematical operators including equals signs) are invisible, and can’t be measured. All information in the world seems to have this format whereby only these types of mathematical categories are measurable. And as opposed to an equation written on a piece of paper, these categories, relationships and numbers have real power in the world.
Importantly, the above 3 types of information that characterise the physical world can’t merely exist, because the mere existence of information implies nothing, unless there also exists a knowledge component to the world whereby this type of information is known to the world, or at least known by local parts of the world like particles or atoms or molecules.
But it is clear that life is using the above 3 types of information to build “higher-level” information via the use of logical connectives (represented as (e.g.) IF, AND, OR, THEN, IS TRUE) to collate and analyse the lower-level information, in order to build an accurate picture of its surrounding world, which is so important for survival in the world. But just like the abovementioned mathematical operators and equals signs represent aspects of the world that are powerful but not measurable, the logical connectives also represent aspects of the word that are powerful but not measurable. And the higher-level “logical categories” that can be built, using logical connectives, out of the lower-level mathematical categories, need to be precise and exact in order to build a reasonably accurate picture of the surrounding world. But these “logical categories” are not necessarily measurable in the same way that lower-level mathematical categories of information are measurable. Despite the physical architecture of the brain, including any special molecules and cells, these higher-level “logical categories” of information are seemingly not measurable because measuring instruments can’t account for the logical connectives.
So contrary to what you imply, I think that “numerical exactitude” is always there, and precise mathematical and/or logical categories and relationships exist, but seemingly only the type of mathematical categories that are found in the mathematical law of nature relationships are measurable.