1. Programming in very concrete/practical terms because you do not know how to think in precise and abstract terms (do not know math)
2. Thinking more precisely and abstractly (more mathematical way)
3. Only do some key important abstractions, and being a bit hand-wawy again in terms of precision. The reason: important real-world problems are usually very complex, and complex problems resist most abstractions, and also being totally precise in all cases is impossible due to the complexity.
All-in-all it is due to increased complexity in my opinion.
Example:
1. Writing some fun geometry related programs 2. learn about geometry more seriously 3. write software based on a multiple hundred thousand line CAD kernel.
Other example:
1. Write fun games on C64 2. Learn about computer graphics in University 3. Contribute to the source code of Unreal Engine with multiple million lines of code with multiple thousand line class declaration header files.
1. Programming in very concrete/practical terms because you do not know how to think in precise and abstract terms (do not know math)
2. Thinking more precisely and abstractly (more mathematical way)
3. Only do some key important abstractions, and being a bit hand-wawy again in terms of precision. The reason: important real-world problems are usually very complex, and complex problems resist most abstractions, and also being totally precise in all cases is impossible due to the complexity.
All-in-all it is due to increased complexity in my opinion.
Example: 1. Writing some fun geometry related programs 2. learn about geometry more seriously 3. write software based on a multiple hundred thousand line CAD kernel.
Other example: 1. Write fun games on C64 2. Learn about computer graphics in University 3. Contribute to the source code of Unreal Engine with multiple million lines of code with multiple thousand line class declaration header files.