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| public:t-709-aies-2024:aies-2024:intro [2024/08/22 10:29] – [Models in Science, Engineering & Math] thorisson | public:t-709-aies-2024:aies-2024:intro [2024/11/04 15:11] (current) – [The Scientific Method: Classical Description] thorisson |
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| | Identification, description and formalization of phenomenon | 1. Observation and description of a phenomenon or group of phenomena. | | | Identification, description and formalization of phenomenon | 1. Observation and description of a phenomenon or group of phenomena. | |
| | Hypothesis, null-hypothesis | 2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation. | | | Hypothesis, null-hypothesis | 2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation. | |
| | Creation of experimental setup to test hypothesis | 3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations. | | | Creation of **experimental setup** to test hypothesis | 3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations. | |
| | Performance of experiment, collection and analysis of results | 4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments. Basic assumption: Repeatability --- Can be repeated by anyone anywhere | | | **Perform experiment**, collect & analyze results | 4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments. Basic assumption: Repeatability --- Can be repeated by anyone anywhere. | |
| | Repeatability requires formal framework | Detailed description, clear goals, clear (limited) scope, hence the formalities in their execution | | | Repeatability requires structured framework | Detailed description, clear goals, clear (limited) scope, hence the formalities in their execution. | |
| | Key idea: Comparsion | Baseline collected in same experimental setup without any other intervention by experimenter | | | Key idea: **Comparision** | Baseline collected in same experimental setup without any other intervention by experimenter | |
| | Key way of comparing | Experiments | | | Key way of comparing | Empirical experiments. | |
| | Bottom line | Scientific research is a //slow and expensive process//. \\ But it's the best one we've got (so far). \\ And it's completely worth it. | | | Bottom line | Scientific research is a //slow and expensive process//. \\ But it's the best one we've got (so far). \\ And it's completely worth it. | |
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| ====Footnote on Terminology==== | |
| | Terminology is important! | The terms we use for phenomena must be shared to work as an effective means of communication. Obsessing about the definition of terms is a good thing! | | |
| | Beware of Definitions! | Obsessing over precise, definitive definitions of terms should not extend to the phenomena that the research targets: These are by definition not well understood. It is impossible to define something that is not understood! So beware of those who insist on such things. | | |
| | \\ Overloaded Terms | Many key terms in AI tend to be overloaded. Others are very unclear. Examples of the latter include: //intelligence, agent, concept, thought.// \\ Many terms have multiple meanings, e.g. reasoning, learning, complexity, generality, task, solution, proof. \\ Yet others are both unclear and polysemous, e.g. //consciousness//. \\ One source of the multiple meanings for terms is the tendency, in the beginning of a new research field, for founders to use common terms that originally refer to general concepts in nature, and which they intend to study, about the results of their own work. As time passes those concepts then begin to reference work done in the field, instead of their counterpart in nature. Examples include reinforcement learning (originally studied by Pavlov, Skinner, and others in psychology and biology), machine learning (learning in nature different from 'machine learning' in many ways), neural nets (artificial neural nets bear almost no relation to biological neural networks). \\ Needless to say, this regularly makes for some lively but more or less //pointless// debates on many subjects within the field of AI (and others, in fact, but especially AI). | | |
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| | What are the main types? | Deduction: All men are mortal. Socrates is a man. Hence, Socrates is mortal \\ Abduction: How did this come about? (Sherlock Holmes) \\ Induction: What is the general rule? \\ Analogy: 'This' is like 'that' (in 'this' way). | | | What are the main types? | Deduction: All men are mortal. Socrates is a man. Hence, Socrates is mortal \\ Abduction: How did this come about? (Sherlock Holmes) \\ Induction: What is the general rule? \\ Analogy: 'This' is like 'that' (in 'this' way). | |
| | How is it used in science? | In empirical science to unearth the "rules of the universe". \\ In mathematics as axioms. \\ In philosophy as a way to construct arguments. \\ In computer science to write code. | | | How is it used in science? | In empirical science to unearth the "rules of the universe". \\ In mathematics as axioms. \\ In philosophy as a way to construct arguments. \\ In computer science to write code. | |
| | Why does it work? | Because the world's behavior is/seems rule-based. | | | Why does it work? | Because the world's behavior is/seems rule-based, some of which we have figured out to date (a very small part!). | |
| | | How is Reasoning relevant to AI & Ethics? | To manage rules requires reasoning. Intelligence makes models of the rules of the physical world. Therefore, reasoning is a necessary part of any intelligence. AI seeks to create machines that contain intelligence, thus AI must seek methods for machines that reason. Ethics can only make sense if it can be encoded in rules. | |
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| | 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. | | | 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. | |
| | \\ 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**. | |
| | All scientific theories seek a model | No matter how explicit or implicit, all scientific theories are models of the world. // Good scientific theories tie a lot of knots, leaving few loose ends. // Best known example: **E=mc^2** | | | All scientific theories seek a model | No matter how explicit or implicit, all scientific theories are models of the world. \\ Good scientific theories tie a lot of knots, leaving few loose ends. Best known example: **E=mc^2** | |
| | Science vs. Mathematics | Mathematics is **axiomatic**: Some a-priori premises are (and must be) known and complete. \\ In contrast, 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) known and complete. \\ In contrast, 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 | Science sees an undifferentiated world and looks for the model. \\ In engineering the model is given; the world is modified to behave like the model. | | | Science vs. Engineering | Science sees an undifferentiated world and looks for the model. \\ In engineering the model is given; the world is modified to behave like the 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 theory 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. | |
| | \\ 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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| | ====Footnote: Terminology==== |
| | | Terminology is important! | The terms we use for phenomena must be shared to work as an effective means of communication. Obsessing about the definition of terms is a good thing! | |
| | | Beware of Definitions! | Obsessing over precise, definitive definitions of terms should not extend to the phenomena that the research targets: These are by definition not well understood. It is impossible to define something that is not understood! So beware of those who insist on such things. | |
| | | \\ Overloaded Terms | Many key terms in AI tend to be overloaded. Others are very unclear. Examples of the latter include: //intelligence, agent, concept, thought.// \\ Many terms have multiple meanings, e.g. reasoning, learning, complexity, generality, task, solution, proof. \\ Yet others are both unclear and polysemous, e.g. //consciousness//. \\ One source of the multiple meanings for terms is the tendency, in the beginning of a new research field, for founders to use common terms that originally refer to general concepts in nature, and which they intend to study, about the results of their own work. As time passes those concepts then begin to reference work done in the field, instead of their counterpart in nature. Examples include reinforcement learning (originally studied by Pavlov, Skinner, and others in psychology and biology), machine learning (learning in nature different from 'machine learning' in many ways), neural nets (artificial neural nets bear almost no relation to biological neural networks). \\ Needless to say, this regularly makes for some lively but more or less //pointless// debates on many subjects within the field of AI (and others, in fact, but especially AI). | |
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