As has been mentioned or alluded to, the underlying premise may well be flawed. By considerable extrapolation, I infer that the unstated intent is to find a reliable method for comprehending mathematics, starting with natural numbers, such that an algorithm can be created that consistently arrives at the most rational answer, or set of answers, to any problem.
Everyone reading this has had more than a little training in mathematics. Permit me to digress to ensure everyone recalls a few facts that may not be sufficiently appreciated. Our general education is the only substantive difference between Homo Sapiens today and Homo Sapiens 200,000 years ago.
With each generation the early education of our offspring includes increasingly sophisticated concepts. These are internalized as reliable, even if the underlying reasons have been treated very lightly or not at all. Our ability to use and record abstract symbols appeared at about the same time as farming. The concept that “1” stood for a single object and “2″ represented the concept of two objects was establish along with a host of other conceptual constructs. Through the ensuing millennia we now have an advanced symbology that enables us to contemplate very complex problems.
The digression is to point out that very complex concepts, such as human logic, require a complex symbology. I struggle with understanding how contemplating a simple artificially constrained problem about natural numbers helps me to understand how to think rationally or advance the state of the art. The example and human rationality are two very different classes of problem. Hopefully someone can enlighten me.
There are some very interesting base alternatives that seem to me to be better suited to a discussion of human rationality. Examining the shape of the Pareto front generated by PIBEA (Prospect Indicator Based Evolutionary Algorithm for Multiobjective Optimization Problems) runs for various real-world variables would facilitate discussions around how each of us weights each variable and what conditional variables change the weight (e.g., urgency).
Again, I intend no offense. I am seeking understanding. Bear in mind that my background is in application of advanced algorithms in real-world situations.
I’m new here, so watch your toes...
As has been mentioned or alluded to, the underlying premise may well be flawed. By considerable extrapolation, I infer that the unstated intent is to find a reliable method for comprehending mathematics, starting with natural numbers, such that an algorithm can be created that consistently arrives at the most rational answer, or set of answers, to any problem.
Everyone reading this has had more than a little training in mathematics. Permit me to digress to ensure everyone recalls a few facts that may not be sufficiently appreciated. Our general education is the only substantive difference between Homo Sapiens today and Homo Sapiens 200,000 years ago.
With each generation the early education of our offspring includes increasingly sophisticated concepts. These are internalized as reliable, even if the underlying reasons have been treated very lightly or not at all. Our ability to use and record abstract symbols appeared at about the same time as farming. The concept that “1” stood for a single object and “2″ represented the concept of two objects was establish along with a host of other conceptual constructs. Through the ensuing millennia we now have an advanced symbology that enables us to contemplate very complex problems.
The digression is to point out that very complex concepts, such as human logic, require a complex symbology. I struggle with understanding how contemplating a simple artificially constrained problem about natural numbers helps me to understand how to think rationally or advance the state of the art. The example and human rationality are two very different classes of problem. Hopefully someone can enlighten me.
There are some very interesting base alternatives that seem to me to be better suited to a discussion of human rationality. Examining the shape of the Pareto front generated by PIBEA (Prospect Indicator Based Evolutionary Algorithm for Multiobjective Optimization Problems) runs for various real-world variables would facilitate discussions around how each of us weights each variable and what conditional variables change the weight (e.g., urgency).
Again, I intend no offense. I am seeking understanding. Bear in mind that my background is in application of advanced algorithms in real-world situations.