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| public:t-713-mers:mers-23:concepts_terms [2023/10/02 13:50] – [Models] thorisson | public:t-713-mers:mers-23:concepts_terms [2024/09/15 09:00] (current) – [INTRODUCTION] thorisson |
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| ====== INTRODUCTION ====== | ====== INTRODUCTION ====== |
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| | | EMPIRICAL REASONING | Defeasible / non-axiomatic reasoning where the data, rules, and results are restricted to the physical world. | |
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| ====Models==== | ====Models==== |
| | **Model** | A model is a "cartoon" of a phenomenon -- an information structure that captures the most important (preferably all the important) aspects of a phenomenon in question. | | | What it is | A model is a "cartoon" of a phenomenon -- an information structure that captures the most important (preferably all the important) aspects of a phenomenon in question. | |
| | All scientific theories present a model | No matter how explicit or implicit, all scientific theories are models of the world. //Best known example: E=mc^2// | | | All scientific theories present a model | No matter how explicit or implicit, all scientific theories are models of the world. //Best known example: E=mc^2// | |
| | Science vs. Mathematics | Mathematics is **axiomatic**: Some a-priori premises are (and must be) assumed. \\ Science is non-axiomatic: We do not know the full set of rules that govern the universe, and we will never know. | | | Science vs. Mathematics | Mathematics is **axiomatic**: Some a-priori premises are (and must be) assumed. \\ Science is non-axiomatic: We do not know the full set of rules that govern the universe, and we will never know. | |
| | Science vs. Engineering | In science we look for the model; \\ in engineering we mold the world to behave like our model. | | | Science vs. Engineering | In science we look for the model; \\ in engineering we mold the world to behave like our model. | |
| | Science + Math | We strive to make scientific theories (models of the world) mathematical because of the //compactness, precision,// and //specificity// this can give us. However, it is not guaranteed solely through the use of math because //a model must detail how it maps to the thing it is a model of//. If this is not done properly the math provides //no benefits//. \\ Mapping a model to its reference: A good scientist does it properly; a bad scientist does it sloppily; the wannabe ignores it happily. \\ Bottom line: Being mathematical is //no guarantee// for good science - it is neither necessary nor sufficient. | | | \\ Science + Math | We strive to make scientific theories (models of the world) mathematical because of the //compactness, precision,// and //specificity// this can give us. However, it is not guaranteed solely through the use of math because //a model must detail how it maps to the thing it is a model of//. If this is not done properly the math provides //no benefits//. \\ Mapping a model to its reference: A good scientist does it properly; a bad scientist does it sloppily; the wannabe ignores it happily. \\ Bottom line: Being mathematical is //no guarantee// for good science - it is neither necessary nor sufficient. | |
| | Science + Engineering + Math: The Holy Trinity | The three fields so defined support each other: Building better scientific models helps us engineer better; engineering better helps us build new tools for doing science better. Both are bootstrapped by philosophy and clarified through math. | | | Science + Engineering + Math: The Holy Trinity | The three fields so defined support each other: Building better scientific models helps us engineer better; engineering better helps us build new tools for doing science better. Both are bootstrapped by philosophy and clarified through math. | |
| | The universe: Nothing is given | How do we know that the sun will come up tomorrow? What evidence do we have? Can we prove it mathematically that the sun will come up tomorrow? \\ The only thing we know for sure is that we can perceive things in the world and that "I am here now". (This principle is most famously captured by Rene Descartes who wrote "I think, therefore I am".) \\ But since that perception is provided/generated by the same universe that we want to claim "exists" through those senses, using those grey cells, we cannot possibly know **for sure** what that really is, and hence whether it can be trusted. \\ Therefore, the universe is (and cannot be anything but) **non-axiomatic**. | | | \\ The universe: Nothing is given | How do we know that the sun will come up tomorrow? What evidence do we have? Can we prove it mathematically that the sun will come up tomorrow? \\ The only thing we know for sure is that we can perceive things in the world and that "I am here now". (This principle is most famously captured by Rene Descartes who wrote "I think, therefore I am".) \\ But since that perception is provided/generated by the same universe that we want to claim "exists" through those senses, using those grey cells, we cannot possibly know **for sure** what that really is, and hence whether it can be trusted. \\ Therefore, the universe is (and cannot be anything but) **non-axiomatic**. | |
| | \\ Computer Science | A creative mix of empirical science, engineering and mathematics. \\ Direct testing of applications and programs; user studies. \\ Models and simulations. \\ Logical and mathematical proofs. | | | \\ Computer Science | A creative mix of empirical science, engineering and mathematics. \\ Direct testing of applications and programs; user studies. \\ Models and simulations. \\ Logical and mathematical proofs. | |
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