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Mathematics, science, and informatics
1. Mathematics, science, and informatics
We are primarily concerned with three areas of study.
mathematics
physical science - reality science
informatics - computer/information science
2. Mathematics
Mathematics is the study of mathematical systems.
Hofstadter: "
Mathematics is what mathematicians do". Hofstadter, D. (1979).
Gödel, Escher, Bach: An eternal golden braid. New York: Vintage Books., p. 559.
Hofstadter makes the claim that mathematics is what mathematicians do. Citing the example of Ramanujam, he goes on to assert that all mathematicians are isomorphic in the sense that they think in the same way. What exactly is that way? In part, mathematicians are able to abstract away details to such an extent that they become the butt of jokes indicating a loss of touch with reality. By the beginning of the 20th century, mathematics as a field had pretty much decided to divorce itself from reality (including philosophical questions) by making mathematics a formal system of symbols and symbol manipulation.
3. Mathematics
Mathematics is abstract and has no direct connection with reality. That was a goal of mathematicians at the start of the 20th century, motivated by the German mathematician Hilbert's 23 unsolved problems in mathematics, posed in 1900.
Any connection of mathematics with reality is left to others - philosophers, scientists, etc.
4. Physical science
Physical the science of reality. The main/basic field of physical science is physics - of what is the universe made, how does it work, how can it be predicted, etc.?
5. Approaches
inductive: bottom-up, do experiments, gather data, find patterns, create theories, etc.
deductive: top-down, create theories, not necessarily based on reality, test and validate those theories, etc.
Which of these primary methods does God use in the Bible? Provide some examples.
6. Historical science
Historical science is science applied to past times.
7. Informatics
Informatics is the field of computer/information science which is a combination of the following.
mathematics (logic, etc.)
physical science of reality
engineering efficiency issues
What does one need to make a computer? (based on Shannon's insight).
8. Making a computer
To make a computer, one needs a switch.
What does one need to make a faster computer?
9. Making a faster computer
To make a computer faster, one needs a faster switch.
10. Efficiency issues
The field of mathematics is not concerned with practical issues of engineering efficiency.
Dijkstra: "The poorer mathematicians had better remain pure mathematicians" (because they do not deal well with practical issues of engineering efficiency)
11. Relationship
So informatics is the use of physical switches to simulate a mathematical abstraction of a computational machine that is called a/an (electronic digital) computer.
12. End of page
